Do central banks need to be "independent"?

Simon Wren-Lewis has a wonkish post, The strong case against independent central banks Mainly Macro 03/05/2016 raising points I'm glad to see being discussed. He gives some background on the development of thinking about central banks and economic management. Here he describes the post-Bretton Woods state of affairs, which Yanis Varoufakis would call the birth of the Global Minotaur. But "delegation" here, he means "giving central banks the power to decide when to change interest rates (independent central banks, or ICBs)":

A story some people tell is that this all fell apart in the 1970s with stagflation. In the sense I have defined it, that is wrong. The Keynesian framework had to be modified to deal with those events for sure, but it was modified successfully. Attempts by New Classical economists to supplant Keynesian thinking in policy circles failed, as I note here.

The more important change was the end of Bretton Woods and the move to floating exchange rates. That was critical in allowing the focus of demand management to shift away from fiscal policy to monetary policy. The moment that happened, it allowed the case for delegation to be made. Academics talked about time inconsistency and inflation bias, but the more persuasive arguments were also simpler. Anyone who had worked in finance ministries knew that politicians were often tempted and sometime succumbed to using monetary policy for political rather than economic ends, and the crude evidence that delegation reduced inflation seemed strong.

And he notes that the conservative-leaning consensus before the 2008 crisis revealed its huge problems to a wider public:

However the consensus assignment had an Achilles Heel. It was not the global financial crisis (which was a failure of financial regulation) but the Zero Lower Bound (ZLB) for nominal interest rates. Although many macroeconomists were concerned about this, their concern was muted because fiscal action always remained as a backup. To most of them, the idea that governments would not use that backup was inconceivable: after all, Keynesian economics was familiar to anyone who had done Econ 101.

That turned out to be naive. What governments and the media remembered was that they had delegated the job of looking after the economy to the central bank, and that instead the focus of governments should be on the deficit. Macroeconomists should have seen the warning signs in 2000 with the creation of the Euro. There monetary policy was taken away from individual union governments, but still the Stability and Growth Pact was all about reducing deficits with no hint at any countercyclical role. When economists told politicians in 2009 that they needed to undertake fiscal stimulus to counteract the recession, to many it just felt wrong. To others growing deficits presented an opportunity to win elections and cut public spending.

Macroeconomists were also naive about central banks. They might have assumed that once interest rates hit the ZLB, these institutions would immediately and very publicly turn to governments and say we have done all we can and now it is your turn. But for various reasons they did not. Central banks had helped create the consensus assignment, and had become too attached to it to admit it had an Achilles Heel. In addition some economists had become so entranced by the power of Achilles that they tried to deny his vulnerability.

And that vulnerability is essentially the conservative obsessions that are part of Hoover Hoover/Heinrich Brüning economics that wound up having a pro-cyclical bias in a depression economy.