First, there's Tether > We're the only option in town. Then, there's Circle > We're more legit than Tether, we're based in the US. Now, there's the banks > We're more legit than Circle, we're banks!
Eventually, the Fed itself will start issuing stablecoins and out-legitimize everyone else.
That would be a CBDC (Central Bank Digital Currency), which the current administration doesn’t seem to want. One advantage of such a CBDC would be that central banks of other countries could be persuaded to use them (for cross border payments and transfers), whereas a stable coin issued and managed by a group of banks would likely not have this advantage (not saying never though).
The point of a CBDC is government control over an increased share of the money supply. Pretty irrelevant to USD balances held by other central banks.
The point of a stablecoin for an entity with an American banking license is... nothing?
That's doubtful everyone else will be out-legitimized ... because ultimately the Fed will issue coins they can fully control (freeze, delete, etc. whenever they wish so). That doesn't make holding such money very valuable. A lot of people understanding this concern will favor USDT or similar privacy oriented coins and thus these coins will keep flourishing (however USDC could disappear for this very reason).