I've just always heard the term "regenerative braking" used with the assumption that the power would be stored or transferred into overhead catenaries for use in getting up the hill.
The issue with your plan is you need a generator good for several hundred watts (basically, what two strong riders can do uphill, you need the brake to do downhill), which makes it big and heavy. If you get rid of that power as heat, you're going to have a toaster element or something similar sticking off the back of your bike somewhere.
My idea is a fan enclosed in a tube with roller that rolls on the tire when engaged, with the tube acting as a brake drum and the fan part blowing enough air through to keep the brake cool, and also using a lot of that energy for blowing the air. But I think the market would be too small for it.
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"be careful this rando stuff is addictive and dan's the 'pusher'."