Cryptopia and Poloniex are probably the only ones who are not asking for kyc and aml, the other ones are all asking for this shit for withdrawing money.
Yes, binance works without KYC as I know. I don't have a large deposit there (usually it's no more than $3000) but there wasn't any problems with withdrawals without verification at all.
Etherdelta is the best exchange that you can use in order to trade and deposit-withdraw as much money as you want, but there are a lot of ico's tokens in there, and they all are crap.
if you want to withdraw a large amount of money in binance, then the best thing that you can do is just upload your documents.