Banks are governed first and foremost by state law. State banking laws are very easy to adhere to. State/local banks do not have to be FDIC insured.
HOWEVER, once the state tries to offer services over state lines (to out-of-state customers, or out-of-state locations), then federal laws kick in. (Federal laws automatically kick in if a bank reaches a certain size.) Federal laws also apply to transactions between banks, where either bank is subject to federal laws (or if one bank is in a different state from another).
Finally, you vastly overestimate the lobbying prowess of national banks. Local/state banks have significantly more influence with politicians b/c they are in-state institutions (i.e., profits get taxed by that state; their executives are local businessmen instead of New Yorkers).