The interesting part to me is that (afaik) you're allowed to go to the auction and bid on your own car.

This is, in my experience as a dealership repossession titles clerk, extremely rare to the point of being non-existent. Might be because my corporation doesn't allow non-auto dealers to attend the auctions in which repos get sold.

And technically, if your car sold for more than you owe + repo fees, they have to give that money back to you (incredibly rare).

It is also highly unlikely that a car sells for more than is owed + the fees. More often than not you're going to have a hefty chunk left to pay after the auction is done. I had a person surrender their vehicle voluntarily (which counts as a repossession type) and it was valued at $6000. She owed $14k on it. My guess is it's going to sell for 8k-ish, leaving her on the hook for the rest.

Disclaimer: I work for a large corporate dealership, this is solely my experience in my day to day job, YMMV.