I do agree that we can't necessarily throw the proverbial baby out with the bathwater, and reject BoD SIMPLY because it's been used and abused to undermine EENS dogma.
I've always separated the two concerns, which are nearly always conflated ... by both sides.
I have objections to BoD theory while examining it as a standalone thing. I see no evidence of its having been revealed, nor any theological proof for it. If you look at its origins, it was CLEARLY rooted in speculation.
St. Augustine was really the only Church Father to unambiguously float the notion, and he was CLEARLY and admittedly speculating. In the famous passage, he wrote, "having considered it over and over again, I find that ... [BoD]". He went back and forth on it, and clearly said "I find that ...". He was clearly not teaching this with any authority, as if it were some doctrine received from the Apostles and part of the Deposit. In fact, the argument he adduced in that passage was mistaken, as he argued from the example of the Good Thief. Problem there, of course, is that the Good Thief died before the Sacrament of Baptism was made obligatory after Our Lord's Resurrection. Nor is it clear what is meant by "paradise", as he could not enter Heaven "this day", since the gates of Heaven weren't opened until Our Lord rose a couple days later on the Third Day. This "paradise" was a reference to the Limbo of the Fathers. In any case, St. Augustine later retracted BoD and made some of the strongest anti-BoD statements in existence. But the tentativeness of his speculation, the fact that it was based on mistaken reasoning, and the fact that St. Augustine later vehemently retracted it ... these seemed to be lost on those who later in Medieval times kept appealing to his "authority" and that of St. Ambrose for their belief in BoD. It was also lost on them that 5-6 Church Fathers explicitly rejected it. What were the other Fathers, chopped liver? When the works of St. Augustine became more available in the proto-scholastic era, there was an excessive adulation of St. Augustine, to the point that the Church had to condemn the proposition that it's possible to prefer the teaching of St. Augustine to that of the Church's Magisterium. When the Church condemns a proposition, it's because someone out there holds it. St. Augustine's theological position that infants who die unbaptized go to hell and suffer an (albeit mild) pain of loss was held for 700 years ... until it was finally questioned by Abelard, and eventually most theologians sided with his opinion. And, interestingly, the same Abelard also rejected BoD theory. I'll come back to an interesting aside about Abelard in a later post.
As for St. Ambrose, it's unclear what he meant about Valentinian. He hoped that the same condition could apply to Valentinian's piety/zeal as would apply to unbaptized martyrs. But he then said that even unbaptized martyrs are not crowned, even if they are washed. That distinction has never been properly noticed or accounted for. Elsewhere, St. Ambrose clearly teaches that even devout catechumens cannot be crowned (enter the Kingdom) if they die before their initiation (reception of the Sacrament). Was he contradicting himself or was there some distinction we're missing?
So these were the only two Fathers who arguably held some notion of BoD, one of them temporarily. We have 5-6 Fathers who explicitly reject the concept. At one point, St. Augustine admitted that BoD was speculation in response to the fact that sometimes devout catechumens would die without Baptism, whereas certain scoundrels who kept sinning until their last moments would receive the Sacrament on their deathbed. So here the speculation was rooted in judgments about what would or would not be "fair" for God to do, a very dangerous line of thinking, as many have lost the faith due to considering God cruel or unmerciful for allowing one or another tragedy to befall innocent people. St. Augustine dismissed this line of reasoning, saying that those who "wish to be Catholic" must reject it, and that this line of thought leads to a "vortex of confusion". He couldn't have been more prophetic. BoD has created an incredible vortex of confusion in the Church, precisely because it's all motivated by this notion that "it would not be fair if ..." Even St. Robert Bellarmine stated that he came to accept BoD because the contrary "would seem too harsh" (durius esset). But this is not theology, and our judgments about the mercy and justice of God from our feeble minds can never be used as theological proof of anything. God's allowing of evil in the world has long remained a mystery. We simply hold by faith that WHATEVER God does is in fact all just and all merciful at the same time. So it is not for us to draw theological conclusions from emotional premises. We are to understand what God has REVEALED to us, and BoD is not revealed. God only revealed the necessity of Baptism for entry into the Kingdom of Heaven. Also, there's this disturbing premise in BoD, that somehow people can be prevented by "impossibility" from receiving a Sacrament that God willed them to receive ... as if anything were impossible for God. It's basically a dark heretical underbelly of the entire thing that St. Augustine also exposed as such in the "vortex of confusion" passage, and that's why he said that anyone who wished to be Catholic needs to reject that thinking. God has worked miracles to get the Sacrament of Baptism to His elect, raising some from the dead (via St. Peter Claver), or providing miraculous access to water. Impossibility is nonsense. Ironically, BoDers claim that anti-BoDers "constrain" God by the Sacraments, while themselves constraining Him by "impossibility". No, we do not "constrain" God by the Sacraments. He can obviously do anything He wills. What we're trying to investigate is what God has revealed about the economy of salvation as He has laid it down.
So, after the time of St. Fulgentius (early 500s A.D.) until about 600 years later, there's no mention of BoD in Catholic theology (for or against). In the pre- or proto- scholastic era, there was the revival of interest in and access to St. Augustine, and there was a dispute about BoD between two famous teachers, Abelard and Hugh of St. Victor, the former being against and the latter for. Peter Lombard, of the famous "Sentences", that became the textbook of all the later scholastics, asked St. Bernard to weigh in on the dispute. St. Bernard VERY TENTATIVELY sided in favor of BoD, saying that he'd "rather be right with Augustine than wrong on his own" ... evidently also unaware that St. Augustine had retracted the opinion. Peter Lombard then went with it, included it in the "Sentences", from where St. Thomas also went with it. And, after St. Thomas, it of course went "viral". On a side note, St. Bernard was very hostile to Abelard, accusing him of impiety (and even heresy) for his approach to theology. But Abelard was nothing but ahead of his time and should be considered the father of scholasticism. His approach in the work "Sic Non" (Yes No) was nothing other than the same approach St. Thomas made famous later, where he examined theological propositions based on looking at the counter-arguments. Abelard also defined theology as reason applied to revealed doctrine, which St. Bernard wrongly rejected as impious. This became the very definition of theology, as taught by St. Thomas and the scholastics. St. Bernard did not think that reason should be applied to Revelation.
Then we have something from Pope Innocent II, who also (as we have seen incorrectly) relied on "the authority of Ambrose and Augustine," but did not teach it with his own papal authority. NEITHER of these Fathers, as we have seen, taught it with any kind of "authority" ... if they even held the opinion at all.
This is the true history of BoD, and there's no evidence that it can be considered any more than mere speculation, often founded in non-Catholic principles, such as binding God by impossibility, judgments regarding whether something or not would be fair for God to do, etc. This thinking, or rather, emotion, is clearly behind BoD theory, and it is not a valid foundation for any kind of actual theology. True theological proofs for BoD simply do not exist.
Finally, I object to BoD because it minimizes the necessity and effects of the Baptismal character. It is the Baptismal character that transforms the soul into the likeness of God's Son, Our Lord, so that the Father recognizes the soul as a Son, a member of the Family of the Holy Trinity, by adoption, and this is how the soul enters into the inner life of the Holy Trinity and can see God as He is in the Beatific Vision. This supernatural ability to see God as He is, human beings lack it by nature, so they require an additional supernatural faculty for it, and that too is an effect of the Baptismal character. This character effectively imprints Our Lord's "DNA" on the soul and the body, allowing human beings to become members of Christ and thus part of the Church. BoD theory would reduce the Baptismal character to a simple non-repeatability marker that some people in Heaven have and others don't, meaning that the Sacrament cannot be repeated. That is not consistent with what the Fathers thought of the "seal" or the "crown" or the "character". For the Fathers, these were essential to entering the Kingdom of Heaven. I'd be more open / amenable to a BoD theory that posited the reception of this character by those who have BoD than the one that holds they do not. There are serious problems with the BoD theory holding that temporal punishment can remain after BoD, since that's not a true "rebirth" as defined by the Council of Trent. There are serious problems with the BoD reading of Trent.
No one denies that BoD eventually became the dominant or prevailing theological opinion, but mere unanimity of opinion does not constitute a note of dogma and revelation. As we saw, St. Augustine's mistaken opinion regarding the fate of unbaptized infants was unanimously held for nearly 700 years. And for the BoDers who make too much of this being the prevailing opinion, many of these same reject the necessity of explicit faith in the Holy Trinity and Incarnation for salvation. Well, what of the fact that this was the unanimous teaching and belief of all the Fathers and of all Catholics for the first 1500 years of Church history? It was OK for a Franciscan and some Jesuit to come along and question this, but evil of Father Feeney to question the prevailing opinion about BoD? If anything could be considered an infallible teaching of the OUM, it's the fact that explicit knowledge of the Holy Trinity and Our Lord were necessary for salvation, and yet the same people who claim was must follow theological opinion of the last couple hundred years, simply toss this aside as if it didn't even exist. Some Trads follow what I call "Cekadism", holding that the consensus of theologians is somehow an effectively-infallible rule of faith. Msgr. Fenton explicitly rejected this exaggeration.
This is really the state of BoD. It is not and can never be defined dogma. There's no theological proof for it, no evidence that it was revealed.
In practice, in its application or, arguably, mis-application, it's caused tremendous harm. If I were pope, one of the first things I'd do is to ban all mention of BoD and order it expunged from all Catholic theological works, including those of the Doctors. It is never to be mentioned again by Catholics ... even short of issuing a condemnation of the notion. Why? Simply weigh the possible good that could come from believing in BoD vs. the harm we've seen come from it.
What good does it do? It's merely used to provide some (possibly unfounded) hope in people who have lost loved ones who were not baptized. That's all it was ever for.
On the other side, it has done tremendous damage to faith in the necessity of the Sacraments for salvation and to EENS dogma. Without BoD, Vatican II could never have happened. Ironically, it also, as Father Feeney famously pointed out, LESSENED individuals' resolve to receive the Sacrament, as they believe it less necessary. So belief in BoD actually lessens the possibility that BoD could "happen". I recall the story related by Archbishop Lefebvre of an African native who urgently requested Baptism, being worried that he wouldn't see the Archbishop for a long time and might die in the interim. Archbishop Lefebvre answered that he needn't worry because he'd be saved by his desire. Did this African go off thinking, "Whew. I don't really need Baptism to be saved." and with a seriously reduced desire and intention to receive it as a result?
BoD needs to be never mentioned again by Catholics, and possibly condemned. If I were Pope, I'd immediately ban any mention of it and order mention of it expunged from all Catholic books, explaining that the Church has never taught BoD, even if it was tolerated, and that the toleration was coming to an end. I would issue an Encyclical/Bull reiterating the necessity of the Sacraments for salvation. Then I would prayerfully consider whether to outright explicitly condemn the notion of BoD, asking God for signs about whether I should do so.