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?