I'd have problems if you did it with something with a long wheel base and obvious wheels, like a typical car. For things like bumper cars and little hover things, the trade-off (able to bump into each other without freaking out; but unable to tilt and roll with what you drive on) would be worth it. It has to be something you could turn around easily, because the thing about player vehicles is that you can just spin around as fast as you want. They should have a sort of square ratio and be silly.
They have their place, certainly. Flat tracks, or perhaps one with jumps which trigger a jumping animation, or open arenas in which to bump into each other; bumper car deathmatch. hmm, yes.
Of course my problem with you doing that is all based on my own perspective, and my ideas about how I use cars in blockland. Please feel free to try whatever you're considering, especially if it means a race in which we can actually run into each other without getting completely stuck or launching into orbit.