Generating a dirty sine wave which will power an appliance is fine, but that's not the goal here. The goal is to generate a clean sine wave which will benefit

Generating a dirty sine wave which will power an appliance is fine, but that's not the goal here. The goal is to generate a clean sine wave which will benefit the grid when applied to it. This is probably impossible at bike workloads, and is in any case quite a bit more of a problem than just throwing an inverter at a DC source and calling it done.