You've said it yourself that according to FDIC insurance, an account can only hold $250k, so what do you think will happen when someone who's account balance is $3k, sudden receives $250k in four hundred different accounts? Your account would be frozen and you would be called upon by the authorites to explain the source of your wealth.
And, once I showed them that I purchased Bitcoin, or other cryptocurrency, for X amount of dollars on X date(s), would that be the end of it? Would the account be unfrozen and my transactions immediately allowed to go through?