There is no pre-existing "system of checks and balances" when it comes to banking. But let's pretend there is.

As an analogy, consider that we have managed to get on with a politically independent Supreme Court, with their least proud moment (Dred Scott) being when they decided to ignore their charter and bow to the will of the people.

I have no problem trusting independent bodies with things, so long as they are well-chosen and truly independent. History shows that this is a much better idea then trusting either the econo-politically elite or the demos.