Two-wheel drive bikes are actually a good idea. Some combustion-engine models actually exist. Mostly dirt bikes. US-based Christini make Honda CRF derivatives with a pretty cool front-wheel drive system. The difference might be hard to tell for people who haven't ridden dirt bikes, I'm not sure, but here's a video that shows a little bit:
https://www.youtube.com/watch?v=si-bI84SZKAYamaha also made a two-wheel-drive racebike prototype. Don't remember the name.
It's pretty interesting to read the ride reports on two-wheel-drive bikes. The handling seems to make a lot of sense ...
