There maybe another problem: banks may not be allowed to make their own currency independent of and distinct from USD (even though it’s pegged to USD initially). The central bank (the Fed) has the monopoly on creatingUSD from nothing.
If banks are allowed to issue their own stablecoin, then yes, I think you are right, it’s going to work. All that a bank has to do then is to partner with Square or some other POS vendor to allow stablecoin holders to spend these anywhere there’s a Square POS. (The bank would have to convince Jack Dorsey who believes in nothing but Bitcoin — for now.)