I'm certain this could be done.
The local university here made an electric minivan a while back - put individual motors on each wheel for all-wheel drive, and lined the floor with batteries. When they were done, the took it out to the local 1/4 mile track and kicked the SNOT out of a Nissan 300 turbo. It was quite funny at the time. (No interior in the minivan, though.)
Remember this - you get to drop the weight of the engine, fuel, and driveline. Add to that the weight of 4 electric motors, a crapload of batteries, and some heavy duty wiring.
Oh - and keep in mind that electric motors generate 100% of their torque at ZERO rpm.
Traction control is easy to build into your control software - simply monitor the RPM of each motor, and drop the power levels on any that are spinning too fast.
I have heard of people running into problems with smog rules, ironically enough. Dunno if this is just urban myth, but I've heard of cars failing the visual for smog because they have no cat - even when they are zero emmision vehicles with no exhaust!