What are the benefits of an independent central bank?

This is a question we've had come up a few times in other threads, and we have never had a real answer to it. <br><br><br><br>Most mainstream economists make the argument that central banks should be entirely independent, with no interference from the state and as much freedom as possible to decide monetary policy as they please. No strings attached. <br><br>These institutions are as much a part of our public infrastructure as bridges and roads.<br><br>Why not? Shouldn't we just nationalise them and make them an important part of the state's fiscal policy? If we did this, wouldn't we be able to set interest rates without worrying about private banks and investors? Wouldn't this be beneficial to the country?