I mean, what would that actually look like? The Fed is insulated from democratic accountability, for very good reasons, but flipside of that is that their powers are intentionally limited. If they had the same immunity to public opinion but with the power to address supply shocks, that would quickly veer into tyranny.
It's a careful balancing act and there is no perfect solution. What's supposed to happen is that Congress acts on supply-shock driven inflation, but this current Congress would rather eat a bag of broken glass than actually govern, which the Fed can't really do anything about.