"This is where we can modify their mandate at any time through legislation."

We really can't. To would so be a fundamental reconstruction of governance, tantamount to constitutional changes.

The central bank running current accounts for citizens and doling out money in a manner similar to how it tries to manage inflation using purchases on the free market etc. is so far beyond the premise of a 'Central Bank' that it's not a 'Central Bank'.

It makes the entity inherently politicized, as it becomes nary impossible to set 'targets' that aren't political.

So yes, we could dump the Central Bank and create a new entity that does 'Central Banking And Other Things' but there isn't even an intellectual framework for that, let alone some kind of reference anywhere in the world that could be used as a guide.

Putting the power of the printing press that close to 'giving out money' in a populist way is pretty scary anyhow and I wouldn't see the point in doing it at all.

If there are progressive social measures to be made, it might be for example related to how we structure what goes on the Feds balance sheet, and why, etc..

If we want to hand out UBI or something like that, it happens under government & the Treasury, not the central bank.