Bitfinex lets you do that, but you have to make a certain minimum deposit to start your account. I think it's about one bitcoin minimum deposit.
You have to verify if you want to withdraw as USD but not if you only withdraw bitcoins. Converting to USD then back to bitcoins is OK without verifying.
Stay out of Bitfinex. That exchange will be collapsing sooner or later. They have been printing USDT without fiat USD backing and they are taking advantage of the fact that the large altcoin exchanges like Poloniex and Bittrex have altcoin/USDT listings.
What they plan to do with all that unbacked USDT, we dont know. But I think the regulators will be giving them a cease and desist order for issuing an unregulated currency.