The main argument against the independent Central bank is that they don’t know what they are doing as can be seen from their track record.

The FED presided over the dot.com bust and 2008, unaware that they were happening and of their consequences.
Alan Greenspan spots irrational exuberance in the markets in 1996 and passes comment. As the subsequent dot.com boom and housing booms run away with themselves he says nothing.
Loans create money and repayments destroy money.
This is what the run-up to 2008 looked like ……
www.whichwayhome.com/skin/frontend/default/wwgcomcatalogarticles/images/articles/whichwayhomes/US-money-supply.jpg
Everything is reflected in the money supply.
The money supply is flat in the recession of the early 1990s.
Then it really starts to take off as the dot.com boom gets going which rapidly morphs into the US housing boom, courtesy of Alan Greenspan’s loose monetary policy.
When M3 gets closer to the vertical, the black swan is coming and you have an out of control credit bubble on your hands (money = debt).
We can only presume the FED wasn’t looking at the US money supply, what on earth were they doing?
The BoE is aware of how money is created from debt and destroyed by repayments of that debt.
www.bankofengland.co.uk/publications/Documents/quarterlybulletin/2014/qb14q1prereleasemoneycreation.pdf 
“Although commercial banks create money through lending, they cannot do so freely without limit. Banks are limited in how much they can lend if they are to remain profitable in a competitive banking system.”
The BoE’s statement was true, but is not true now as banks can securitize bad loans and get them off their books. Before 2008, banks were securitising all the garbage sub-prime mortgages, e.g. NINJA mortgages, and getting them off their books. Money is being created freely and without limit, M3 is going exponential before 2008.
Bad debt is entering the system and no one is taking any responsibility for it. The credit bubble is reflected in the money supply that should be obvious to anyone that cares to look.
Ben Bernanke studied the Great Depression and doesn’t appear to have learnt very much.
Irving Fisher studied the Great Depression in the 1930s and comes up with a theory of debt deflation. A debt inflated asset bubble collapses and the debt saturated economy sinks into debt deflation. 2008 is the same as 1929 except a different asset class is involved.
1929 – Margin lending into US stocks
2008 – Mortgage lending into US housing
Hyman Minsky carried on with his work and came up with the “Financial Instability Hypothesis” in 1974.
Steve Keen carried on with their work and spotted 2008 coming in 2005. We can see what Steve Keen saw in 2005 in the US money supply graph above.
The main argument against the independent Central bank is that they don’t know what they are doing as can be seen from their track record.
 
h/t  Batman11