they went on tilt as soon as they lost the Bishop

I did not actually consider this but by pretending I'm playing as white it definitely feels difficult to accept the loss.

Yeah it's just painful and embarrassing to lose a piece so early. And in such a silly way (although there aren't many non-silly ways to lose a piece on move 8). And then it's not very fun to sit and stare intently at your own foolishness for five or ten or thirty minutes to figure out what the least bad choice is. Part of you just wants to call if off right now so you can start a more fun game already. But failing that, you can just sort of check out and play on autopilot. Of course strong players have been there before and know how to handle it (and they also know they'll wind up even more frustrated if they compound their first mistake) but I think anyone would have a little trouble playing normally afterward.

Honestly I'm not sure how White should take on b5; and I'm not really the best person to ask. I think though after 8.Bxb5 axb5 9.Nxb5, White's Bishop and Knight are stuck in this awkward tangle you mentioned. That needs a couple moves to sort out, and it just looks like one more problem you don't need.

The advantage might be that according to conventional wisdom, you want to avoid trading pieces when you're down material? (Because more pieces on the board mean more complications and more chance for mistakes, which is good news; you need them to make a mistake more than they need you to. Also 7 pieces against 6 is a bit less scary than, say, 2 against 1.) But it's not that big a trade and you're not that far down. Tying your pieces in a pretzel to prevent this seems like an overreaction; perhaps just a slightly more sophisticated form of panic than seen in the game.

The only other thing is, after 8. Nxb5 axb5 9.Bxb5 Rxa3 can Black pile up pieces on the a-file to attack the a-pawn, which in the other line could have been blunted by playing a4? But a4 would have been yet another defensive move after Bb2 and Nc3 or whatever. If I have to deal with Black playing against me on the a-file either way, I think I prefer the way where my pieces are comfortable and I can try for counterplay in the center, instead of just defending passively on the Queenside. But that's a gut reaction with no real calculation behind it.