The thrust of my comment is that resolving bad debt isn't merely a painless exercise in monetary policy. Resolving the bad debt requires somebody to absorb those losses through reduced future consumption. Who absorbs those losses is essentially a matter of public policy, not monetary policy.
The only thing that is special about a central bank is that their special relationship with the government exempts them from the regulations that apply to other banks. However, they still have a balance sheet with debts, which are deposits with the central banks and federal reserve notes (cash) and assets which are assets and loans that have been purchased on the open market.
The central bank also has a small amount of capital which is the ownership stakes of the member banks. Half of which is on deposit with the Federal Reserve and half of which isn't invested but can be called if required. That ownership stake has a guaranteed 8% return (and an effective 16% return) which is a nice deal if you can get it.
Due to its special status a central bank can't be subject to bank runs or be forced into receivership by regulators but it can still be balance-sheet insolvent. And a balance sheet insolvent central bank is a wounded central bank because it loses some of it's ability to control monetary policy through reducing its balance sheets.
In severe deflationary conditions a central bank may take more risks that may put it in a position of being balance sheet insolvent. For example, through the purchase of long term zero coupon government bonds at face value. The effect is to tell the markets that the central bank is putting a ceiling on interest rates long term regardless of inflation which encourages speculation.
Ultimately if a central bank has a consequence free way of creating all the money they needed at will their would be no need for taxes because the central bank could just give the government all the money it wanted.