as a historical matter, the uk has had its bank of england as long as any country and seems to have been as stable as any other.
so i don't necessarily see central banks as a major factor in instability. especially these days. at a guess and without much study, i'd say independent central banks are mostly a stabilising force. i'm thinking of the bundesbank in post-war germany, the boe and the fed, in particular.
certainly there are exceptions. banks do sometimes pursue wrong-headed policies (eg the gold standard). this can lead to the loss of reputation (eg in weimar germany). and sometimes there is interference from politicians (eg zimbabwe).
but a well run central bank adds value, in my view.
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