Here's my 2 cents. I loved Rollcage Stage 2 growing up, and throughout the game I it was fun seeing what sorts of things the AIs would try, and I would frequently be struggling against one or two AIs who were good and/or had good cars. But because every race was different, and that meant different cars, the cars that gave me the most trouble would be different each time. So instead of saying "YOLO420 is going to win unless..." I would think "that red Genesis is going to win unless..." and I think the continuity of characters would be great for identification and getting emotionally attached.
One thing that I think would be important, however, is that (just like players) each AI character is not limited to a specific car. To take the Mario Kart games as an example, in Mario Kart 64 each character had their car and that was it. Bowser always bumps Toad aside. But in the later MK games, such as Mario Kart Wii, characters could choose their car. Instead of 'Bowser always pushes Toad,' it became 'Bowser pushes Toad unless Bowser is in a bike and Toad is in a kart.' Allowing characters to choose different vehicles increased the diversity of interactions they could have with other characters, which I think made the game a lot more interesting.
One way you could do this, is that each AI character is predisposed to a specific selection of cars and/or in-game strategies. Maybe David only plays Vostok cars, or Bob plays random tier 1 cars yet mysteriously remains competitive, or Eric likes to mirror the car you're using. Maybe Fred goes for all of the shortcuts he can, regardless of the fact that his car may not be able to make each one. I think this sort of system would be great. Maybe during single player, the game restricts you to a subset of the AI characters until you beat ____ level or go to _____ region, so that you're forming ideas and opinions of the specific AI characters as you go through the game.
TL;DR I'm in favor of having characters who are not tied to a single car, particularly if they have semblances of personalities.