It really doesn't. You are thinking about the wrong thing. If we were talking about something like duplicate lines of code being eliminated because they could instead refer to the one instance where it pops up, it would apply.
Having multiple instances of the car model doesn't allow that, because the game still needs to render all of those assets individually (in essence, as far as the game engine works, the cars are not the same model), so there are no performance benefits to loading just one model and pasting it around unless the model itself is lower detail than a different car would be (for example, if a NASCAR is less detailed than a Corvette by itself, two NASCARS would be less taxing than a NASCAR and a Corvette only because the total poly count is less).
Just about the only difference it would make resource-wise is that it wouldn't have to load the models individually at the start of the race, and PD could implement a way of loading the single model and duplicating it to the number/textures needed instead of loading the model multiple times so race load times would be faster; but even then I doubt the benefit would be that great.