I think what you're describing is pretty much a CBDC.
Or also, knowing that stablecoins are different from crypto assets which do not have assets as backings and are more volatile, will in the future, the success of stablecoins not call for something like a bank or a recognized office building built to show legalization and acceptance as a means of payments for transactions and services?
I don't think it even matters much of stablecoins have their own bank. What matters most is that they have proof that these stablecoins actually have a 1:1 backing on whatever bank as long as the bank is decent.
I just want to point you to a core difference between Stablecoins And CBDCs according to;
https://www.ccn.com/education/stablecoins-vs-cbdcs-similarities-and-differences/Stablecoins are often distributed by private organizations or businesses. Various types of oversight may include self-regulation by the industry.
Whereas, CBDCs are issued by central banks or governments and are strictly governed and regulated by them. Stablecoins is the pillar of decentralized finance, DeFi.
Historically, BTC has served mainly as a passive store of value, not actively involved in DeFi security or commerce. Yet, much like ETH's dual role in securing Ethereum and serving as currency, bitcoin has the potential to evolve into a versatile asset beyond the base Bitcoin chain.
DeFi is the environment that facilitates Bitcoin transactions between two individuals or parties.