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I never understood why Wankel engines aren't paired with continuously variable transmissions so that you can keep the engine at a constant rotational rate. Many of the issues with Wankels (gas mileage primarily, as well as emissions) are eliminated when tuned to a specific RPM.

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The thing to remember about a CVT is that it's held together by a rubber band. Materials engineering has gotten very good at making stronger rubber bands that don't snap under hard use, but the application you have in mind sounds like an awful lot of wear and tear for a rubber band to undergo.

And, if the whole setup is tuned very specifically on the CVT working properly and the rubber band goes snap, that could be a bad thing.

CVT's in automobiles rely primarily upon metal chains for drive, not rubber bands.

They are sort of metallic rubber bands.

There's also these toroidal Centroid continuously variable transmissions. But they rely on friction and have small contact surfaces. http://auto.howstuffworks.com/cvt3.htm

CVTs have only improved in the last decade (and only so much). The real big push for the rotary started during the late 60's. Transmission technology back then was lacking. Plus you did not have effective electronic engine controls.

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