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@lae
Shaft drive - constant-velocity joints on either end of the shaft so that the steering can turn, and the shaft is splined telescopic (like a car's propshaft) to allow steering/suspension movement. It also reduces unsprung weight (which is good for suspension) because the cranks/riders legs are independent of the steering/suspension. Also it'd be pretty uncomfortable to ride if your legs bumped up and down with the suspension!
I designed that way so that people of different sizes could ride it - I figured that someone wouldn't want to spend £2-3k on a car-replacement vehicle that their other half can't use because he/she is too tall/short. The seat adjusts up/down and the cranks move fore/aft so anyone from about 4'6" to 6'6" can use it.
The losses in converting mechanical to electrical and back again would be pretty high, I imagine. That's not to say that it wouldn't make a workable and useful bike - it would certainly be easier on the knees/less stress on the body (perhaps good for cycles designed for disabled people/people who have limited movement). Chain drive is around 98% efficient which is pretty hard to beat, but crank-to-wheel efficiencies go down quite a lot when using derailers/hub gears - so in the near future we might see electric drive bikes as technology improves.
Hydraulic drive is an interesting option - the losses are lower than current electrical (pun intended) and you only need a few pipes going from the cranks to the wheel rather than a chain/shaft.