Sure, state agencies can and do exist. For enforcement of laws that impact those states' residents. No further. But key banking laws/ regs are Federal bc the banking system is massive and underpins everything. There's a compelling reason for Federal jurisdiction. Most banks are Federally chartered bc they need to be able to do business everywhere, and a state agency has limits on enforcement.
State laws/ regs have borders. If we went to state laws/ regs and agencies only, here are examples of what happens: 1) charter a bank in State A. State A has no rules specific to Banks. Bank does business nationally. No one can force anything systemically bc no laws or regs apply to bank. 2) charter a bank in State A. State A has rules/ regs. Agency in State A can't sue Bank about what happens to residents of State B bc residents of State B do not get the benefit of laws in State A - much like (in an individual criminal context) State B could not prosecute State B residents for violations of laws of State A. That's (roughly, and simplified), how jurisdiction works in the US.
So...have 11 or 33 or 50 different agencies trying to enforce Federal laws (or up to 50 different sets of newly comprehensive state regs/ laws, if you toss Fed law/regs altogether) rather than one, each with far less ability to cause change or enforce compliance with laws about responsible practices, or even agree on what is "responsible banking"?
Having state agencies jockeying to hold banks to a million new state laws (with or without the Fed ones) would be absolute chaos. And if you think it's over-bureaucratic now...you have no idea.