Therefore your quote by Pope Pius XII does not detract in the slightest from what I said.
The quote was not intended to detract your statement in any way. On the contrary, we both agree that saints and theologians in isolation are not infallible. Not saint, bishop, or theologian is the binding teaching authority of the Church. The disagreement resides in that you say that BOD is infallible dogma because of an apparent "consensus" in the Church; when it is not.
No Pope, Council, or theologian says that Baptism of Desire is a sacrament. Likewise no Pope, Council, or theologian says that Baptism of Desire incorporates one into the Catholic Church. BOD does not imprint an indelible character on the soul and the obligation to receive Baptism by water remains.
Session 7, Canon 4 of the Sacraments in General from the Decree Concerning the Sacraments (March 3, 1547):
If anyone says that the sacraments of the New Law are not necessary for salvation but are superfluous, and that without them or without the desire of them men obtain from God through faith alone the grace of justification, though all are not necessary for each one, let him be anathema.
Notice that BOTH Faith and Desire are necessary for justification, not only Desire and not only Faith. It is very clear in Trent that both are necessary. It is not a "OR" proposition but an "AND". As a matter of fact, in claiming that Trent teaches ONE OR THE OTHER (Faith OR Desire), you turn Trent's statement into a heretic statement that Trent itself anathematizes because then you are claiming that
water alone without the will or desire is sufficient to justify, which was condemned as heresy in the canons.