Basically the ones which require documents only do it for 1 of 2 reasons.
1) You won a large amount and they don't want to pay you. Hence they make you show documents which they know most people might avoid showing. And they get away with having to pay out winners. Only scam casinos do that.
2) if you've got some tainted BTC and you try to mix it by a casino site, then they will usually flag this and request for documents.
There are a lot of cases in which scam casinos like Sportsbet and Bitcasino have kept people money. About more than one year ago they kept 21 Bitcoins from a player where he had deposited 15 Bitcoins and won 6 Bitcoins playing. They come up with different excuses from tainted bitcoin to requiring KYC/AML procedures.
I wonder how do casinos know that they are tainted bitcoins even if they really are, the user may have mixed them perfectly. I believe casinos who do this don't want to pay the user.