The Fed does not have the mandate to do what is convenient for the budget. That's not their problem. Obviously this is naive and I'm sure the Fed is under all kinds of pressure, but the Fed is supposed to kill inflation by raising rates to whatever it takes, as long as they don't kill jobs at the same time. The government is supposed to figure something out themselves.

You could also just reduce the money supply by abolishing QE and introducing negative interest rates on liquid deposits and cash.

Then everyone can run a balanced budget and watch their debt melt away.

The reason why we have price controls aka the zero lower bound of interest is that we would rather become eternal debt slaves (money supply has always been growing exponentially even under a gold standard) than face nominal losses that force us to face an umcomfortable truth that from this point onwards you will never earn anything again from owning abundant physical capital and that you will have to work for your own money instead of making others work for it.