In 2009 a number of prominent economists signed a petition arguing for central bank independence. I was less enthusiastic writing:
There is nothing magical about independence that makes for low-inflation.
…The primary reason that independent central banks are better at controlling inflation is that absent direct political control the default selection mechanism favors bankers, i.e. lenders, people whose interests make them more favorable towards lower inflation.
Thus, independence is a political decision that favors lenders in the decisions of monetary policy. Now, depending on the alternatives, there may be good reasons for making this choice but we should not fool ourselves into thinking that we have depoliticized money. We should not be surprised, for example, that "independent" central banks tend to make lender of last resort decisions that protect banks and bankers.