I've seen bikes that had joysticks before, but they were push = left , pull = right type, and I believe handling was not good. I think a Windcheetah joystick would make balance difficult and not offer enough leverage.
In my opinion, handlebars cotribute more to balance and steering dampening than we imagine - I can ride a bike with handlebars no-hands, but not a bike without handlebars...
...What do you mean, you've never tried that?!