Binance's .com platform still allows you to freely withdraw funds worth 2BTC per day. It's their Binance Jersey (fiat) platform that requires people to walk themselves through AML/KYC verification.

I do have to point out that any exchange that still allows people to withdraw funds without AML/KYC, could stop offering you that privilege tomorrow if it wanted, and your funds will be stuck inside until you submit your personal information and whatnot. In other words, the risk is there that these exchanges will turn into the next Bittrex and Poloniex.

It's important to make a rational decision before you sign up to an exchange just for the sake of not having to deal with AML/KYC; do you really want X or Y exchange to have a copy of your ID or passport in case you are locked out and forced to do provide it to them? If not, then definitely skip it.