Cutting out other forms of collateral is where stablecoins can drive up treasury demand. Currency swaps and other credit instruments are huge in repo markets, as is rehypothecation of the same underlying collateral. Stablecoins don't hold claims on treasuries, they hold treasuries. They don't hold gilts and forex swaps, they hold treasuries.
There are problems that come with some of the solutions here, as there mist be as the whole game of fiat is a game of jenga. But short to moderate term they can seem to cannibalize demand for other collateral and chains of rehypothecation in order to reduce treasury yields.