Central Bank Independence to create 'Economic Stability'

I've taken some interesting points from article in which Ben Bernanke states Central Banks must keep their independence in setting interest rates. 

"Restricting banks' ability to execute monetary policy would lead to economic instability and "boom-bust cycles."

The Bank of England has been independent since 1997. Since that time we have witnessed the largest credit boom and bust since the Great Depression. Through all those prior years monetary policy was driven by the Governments Chancellor. So how does a Central Banks independence solve the boom bust dilemma as claimed above?

"Politicians generally prefer holding interest rates low, as a means of stimulating the economy and boosting jobs."

Remind me what are interest rates at now as I write? 0.5% of a percent, the lowest in the BoE's 300 plus year history, since it was established in 1694. I don't think we can actually go much lower, can we? Inflation, as measured by RPI is the highest since our last recession and these guys still have their foot to the floor.

"Thus political interference in monetary policy can generate undesirable boom-bust cycles that ultimately lead to both a less stable economy and higher inflation,"

You don't have to be an economic wizard to see the anomaly in our present time.

How anyone listens to these Monetary planners is beyond me. Markets don't need people like this, something Hugh Hendry states quite aggressively in this video. Markets should 'purge the system of its rottenness' - now there's an idea? What wrong with entities going bankrupt? Its what differentiates real market economies to socialist dictatorships. It frees up resources to meet peoples genuine needs, one of the reasons we live such a relative pleasurable existence. As Mr Hendry states, 'We can spread this over 20 years or we can spread it over 3 years'. My bets are on the former.