My searches have not turned up anyone selling a bicycle with a
continuously variable electric transmission. I don't mean an electric
scooter: I mean one in which the crank turns a generator/alternator,
whose output through an electronic controller then drives an electric
motor on the wheel rim(s) or in the hub(s). There would be no chain,
derailleur or gears, except perhaps for some fixed-ratio gearing inside
the generator/alternator or motor assemblies. A control equivalent to a
shift lever sets the ratio between crank torque and RPMs, which can be
varied over some wide range. The rider sets the speed by changing this
ratio and/or the crank RPMs as they find comfortable. Scooter-type
assist would be possible through use of an optional battery. (Earlier
threads on the subject addressed mechanical CVTs and auto-shift
mechanisms, not an all-electric transmission.)

What's the point? Mostly geekiness, I suppose, but the effectively
infinite number of "gears" while reducing the number of moving parts is
appealing. Also appealing is the notion that a battery in the system
would provide load-levelling (hill assist) but with the rider still
ultimately providing all of the energy, unless of course the rider
cheats by re-charging the battery from an external source. For
non-cheaters :_ the battery need only be large enough to help climb one
hill. Efficiency would not be as good as with a conventional drive, but
that's not really a concern for commuters or pleasure riders.

Surely by now someone must make such a thing?