In principle, I like this idea, but I'm not sure how well it would work in practice. It certainly needs significant thought.
Car damage should be persistent ONLY for GT Mode. For Arcade mode, there should be no persistent damage and you should always start a race with a new version of a car. A lot of people will want to smash up cars just for the fun of it. What should happen when a car is written off (should premium insurance coverage pay / buy new car / how does this affect cars available in Arcade mode)?
Car sales / trading / auctioning would need to be given some serious thought as cars could be sold / traded / auctioned in a damaged state. GT PSP integration would presumably be just one way, from the PSP to the next gen console (PS3, PS4, etc).
I think GT is too hard for most people. The game really needs 2 skill levels that could merge in with Standard / Professional (phyiscs)... In Professional (normal) mode, I'd be game for pretty much any realistic option that anyone mentions. In Standard (easy) mode... Damage shouldn't be persistent. Also, gamers need to be able to resell a car back to the game for something much nearer the original purchase price (but NOT to other gamers, auctions, etc). This would make the game more appealing to kids and car novices who are learning about cars with the game. I think this sort of easy mode is a better solution than the 1 button driving that's being pushed by Turn 10.