The only aggregate alternative to holding T-bills is to hold dollar bank accounts. At which point the bank holds the T-bills instead or the Fed does as balancing assets to the account liability.
It could all be refinanced to three month bills without any issue at all.
Ultimately balance sheets have to balance. In a floating exchange rate system there is no aggregate out.
You are correct on the mechanism here. But my point is adjacent to that. Whilst you always get a buyer for the debt (here the bank), it is the yield that matters as the re-financing cost cannot be escaped irrespective of the owner.
It could all be refinanced to three month bills without any issue at all.
Ultimately balance sheets have to balance. In a floating exchange rate system there is no aggregate out.