The Fed follows regular accounting practices. It doesn't give away its services. However you are ignoring where Fed profits end up.And there is your folly. I really liked your opening line of your response here.
But after that, you fell down.
I never suggested, in any shape or form, that the Fed determines the amount of money for borrowing. But when Congress comes knocking, the Fed comes answering, charging the US treasury interest on the money it borrows from the Fed reserve.