Crypto payments and fiat elimination will happen in the future, but I'm not sure if a stablecoin will be chosen. That depends on the government, we don't have the power to decide.
Stablecoins are not controlled by the government per se. They're just issued by private companies with their own interests. If a stablecoin fails, don't expect the government to respond by making depositors/investors whole again (unlike USD deposits at a bank which are insured by the Federal Government). I'd prefer decentralized stablecoins as they're usually managed by an organization (DAO). Not a for-profit company that serves its own interests instead of the community. DAI and USDJ seem to be the only collaterized stablecoins that are decentralized. The rest are simply algorithmic and subject to failure.
BTC is better off as a store of value due to the way it was designed (deflation). But if volatility disappears, then it would've been another story. That is if Bitcoin is able to scale to meet the demands of everyday users. No one can predict the future, so let's hope for the best. Just my thoughts