But a rich minority would. A rich, motivated group of single-issue activists is political white phosphorous. To say nothing of the fact that the main beneficiaries of such regulation would said minority. The disinterested majority doesn't have much downside if cryptocurrencies go to zero.
If they were rich before cryptocurrencies, they shouldn't care (unless they unwisely bet the farm on it); and if they're rich because of cryptocurrencies, no one else should care, because if cryptocurrencies crash, they wouldn't be rich anymore.
Not as much as some people think. We've been on fixed-supply currencies before; built empires, waged wars, and administered continent-spanning states on them. America has experienced inflation without banning the ownership of gold or foreign currencies. (And repressive states have survived, even thrived, after doing both.)
If the U.S. Treasury started issuing debt and accepting tax payments in Bitcoin, it prompt a rocky transition. But it wouldn't be unprecedented. Switching to a multi-currency regime would create a short-term (as in generational) boost in compensation for financial professionals, as the entire morass of financial plumbing gets re-written and overhauled. Players closely tied to attributes unique to the U.S. dollar, like printers and SWIFT, would die. Players operating at higher levels of abstraction, securities houses and depository banks, would do quite well. Assuming Bitcoin continues deflating, lenders would do phenomenally.
That seems like a stretch. Most people wouldn't care, and the institutions that own it haven't bet that heavily on it. It's a fear-of-missing-out trade for the most part.