i'm sure that is deep solace when you lose half of your savings to inflation. btw not sure which central banks you're thinking of, but this checks and balances stuff does not apply to the fed at least; it is explicitly defined as independent (ie unaccountable).
accountable in the sense that it approves appointees and receives reports, not in the sense that congress or voters have any say in monetary policy decisions. this is literally the point of the fed, to put it outside of electoral politics so it is not subject to democracy.
The Fed has a public mandate, and the Congress has the responsibility and the power to make sure that it fulfils such mandate. Therefore it is accountable and it is subject to democracy, and at the same time independent from the electoral cycle.
