However, I do not think there can be any disagreement that central bank governors need experience with the overall economy. Former Fed chair Bernanke and current chair Yellen both served as Chairs of the Council of Economic Advisors, and there are many Fed directors who have worked in the White House.
In the case of the most independent of central banks, Bundesbank, former governor Weber and current governor Weidmann have both served as economic advisors to Prime Minister Merkel. This testifies to the importance of governors gaining experience on the overall economy and on politics by working with political leaders.