In practice central bankers are unelected politicians. Their mandates are set by politicians, they aren't actually bankers in the normal sense of the term, and what they do is attempt to plan the economy in service of politically set goals. If central bankers were really independent of politics then they would of course have refused to print any money to fund COVID measures like lockdowns on the grounds that they are responsible solely for inflation and employment, so if governments wanted to do that they'd have to pass emergency taxes. Obviously no central banker said that. They were all immediately on board with letting politicians do whatever they wanted.