To be honest I don’t know enough about the mechanics of the Treasury but wouldn’t they be using those funds to pay for gov’t expenditures, war, etc. Otherwise why would a treasury agree to pay interest for dollars their not using?
Also, dollars recieved by individuals, companies, etc that get deposited would have an affect in that the banks don’t lend out the same as they have on deposit. We have a fractional reserve banking system so the amount lent is multiples of the deposit.