"The rider pedals a generator, which replenishes the battery, "

The chain is probably to keep unsprung weight low. Hub motors are not the best for comfort.

Why is that? Do you want sprung mass to be heavier or unsprung mass lighter?

I see how lower unsprung mass could be easier on the tyres but I have no idea how it could impact a rider who's isolated by full suspension.

Sort of both, lower unsprung mass means the wheel moves more easily up and down without the rest of the vehicle doing the same.