He discusses the reasons for this in some of his talks. He was ordained in the new rite in Latin and was convinced of its validity, at least in Latin. He knew personally the Cardinal who ordained him and was satisfied as to the orthodoxy of his beliefs. So under these circuмstances it would have been sacrilegious to repeat the ceremony, even conditionally.
Well said! Although he did not believe he needed to look into it, he did look into it and could not prove his own ordination was doubtful or invalid, nor could +ABL and the others as Byz states below.
Unless Fr. Hesse is dishonest (and I see no reason to think he is, and you don't either), he's said that Archbishop Lefebvre, Bishop Fellay, *and* Bishop Williamson all said that his ordination was valid and he didn't need conditional ordination. I get that sedes would categorically disagree with this outright, and usually would out and out say the new rite is invalid (though I realize you'd more say it was doubtful than straight up invalid I think.)
Honestly, after seeing your comment here, and pondering it, I'm wondering if perhaps the gap between sedes and other trads may be even bigger than previously thought.
The gap here is that the Catholic Church initially always presumes validity unless proven otherwise, whereas the sedes always presume invalidity.
In one of his talks, he talked about his ordination, saying:
"...I have been ordained, unfortunately in the new rite of ordination, but thank God in Latin, everything strictly by the book and +ABL said that would be valid, +Fellay said it's valid and Fr. Franz Schmidberger who is my present superior in Austria says it's valid and +Williamson said there's no need for conditional ordination..."