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They do make class D amps that are RMS continuous rated at several KW. But you have for it, several hundred to thousand. In the end, if you're going to spend $600 on a 3KW class D you might as well spend $600 on a 300A controller, more purpose driven, lower chance of failure (not that the amp would fail, but using it for what it's not made could cause premature failure).
But I like your thinking, as a small class D rated at 500W continuous would handle a bicycle sized motor easily, albeit at the cost of a huge "controller" and added weight. Potential to be super cheap though. Better option than on/off switch.
I'm going to go research >3KW D amps now, just because I'm curious.
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