The short answer is that the standard inflation control model can be done through either monetary or fiscal policy, but monetary policy is depoliticised enough that it's easier to do it there. Doing it through fiscal policy by raising taxes, especially at the top end, is just too politically infeasible.
(also, this process does not in and of itself transfer profit to banks! the bank's margin is generally a fixed number on top of the floating central bank rate)
(also, this process does not in and of itself transfer profit to banks! the bank's margin is generally a fixed number on top of the floating central bank rate)