I think you need to look at your bank. My bank will only let you take out $250 per day from an ATM, only use $1500 max on a single purchase with your debit card. I am thinking of changing banks for this reason.
With rates so darn low, what is the advantage to letting the bank hold your money, besides the convince of paying bills?
Also, yes we have FDIC. But if that is needed, you won't be the only one who needs it. It will be a large pool of customers all at once. So there will be some issue getting your FDIC reimbursement in the event you might need it.