While I can’t speak for everyone, I think that it’s precisely the people who have been mended by their belief in PSA, that can’t bring themselves to question it, or look at other atonement theories. For them, PSA is the very marrow of the Gospel.
I think in their eyes it is the solution to man’s problem which is primarily a judicial problem - hence the need for a legal accounting. As it turns out, this point of view can also be effective in saving a person from their sin (not merely from a legal standpoint, but a practical reality). I think it comes down to a person loving much because s/he feels that s/he has been forgiven much…even more than that, s/he has been given much - a perfect righteousness.
Yes, there are some logical inconsistencies - primarily in the PSA purpose of the crucifixion as you pointed out. But, you know what, not everyone will agree with you, or I, on that. For the particular group of people I have in mind, the blood-sacrifice of the Son of God IS the most beautiful event in History. And, I would trace this back to PSA believers having an unjust view of justice. There is something in our nature that demands appeasement when we are wronged - the guilty MUST be punished, ie, they must suffer in proportion to the suffering they have caused. An eye for an eye, a tooth for a tooth. If this is justice, and, it is just and good for God to punish the wicked, then, Jesus taking our punishment for us is perceived as an act of great love and mercy. I think this recognition, on the part of PSA believers, can effect radical transformation.
So, as long as justice is perceived this way, PSA is the only solution. You lose that, you lose the Gospel. That’s why some people are so terrified to explore different atonement theories. I know I was. However, if one sees justice for what it is (which I will define as an act of mercy towards both the offender AND the one offended), PSA becomes despicable and futile, and has no power to effect change in one’s life. On the contrary, it is God’s mercy towards the offender, in freely forgiving their heinous offenses, and healing him/her from the malady of sin, that ignites radical heart-change, driven by love —At least, that is what I have seen happen to those who do not believe in PSA. For me, well, I don’t know where the heck I am