Is it possible stable coins could have their own bank since they are backed by a country's currency like the U.S Dollar which they use to maintain a stable value?
Or also, knowing that stablecoins are different from cryptoassets 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?
Why not? The world is getting more digital and with the acceptance of cryptocurrency in many climes, there is no way some banks will not be transacting in the USDT and it will be easier for them if their country is such that is crypto-friendly. But this will be cryptocurrency banks because there are wide distinctions between the USD and USDT, and I can't possibly think that any central bank would want to mix that up. First, it is the USD that can back the USDT and not the other way around. Also, the fact that the central bank can not oversight and control the USDT, they will not be able to allow the regular commercial banks to get involved in such.
However, special crypto banks will be doing that, and I believe it is already happening with the current ones, though I have never used them before to know their mode of operation. Nevertheless, for a bank in China to involve itself with illegal underground USDT operations in a country that frowns so much on cryptocurrency means that even the commercial banks that are dealing with fiats will still try it despite knowing that it will never gain the support of the central bank.
Link:
https://www.theblock.co/post/294777/china-busts-1-9-billion-underground-banking-operation-using-usdt