I took very large amounts 10k+ without a problem from my bank many times. This is not an issue where I live / my experience. If a bank ever told me I could not withdraw my own money I would close the account and have them write me a bank check for my balances. I did not even know this was an issue for people until now.
EDIT: ATM withdrawal is a different story. With my bank I can set the max amount ahead of time but there is still a max amount. If I recall it 5k or less. But what do you expect out of a machine.