Is it sensible to require JM makers to do some proof-of-work to disincentivize the destruction of the market by the volunteers?
No, I don't think so.
If there is more supply than demand, the price drops. That's normal, healthy, and to be expected.
You seem to be suggesting manipulating the market to force the prices to be higher than the market supports on its own. If we're currently short of "takers" then low prices is what we need to attract more of them, wouldn't you agree?