Users should be most concerned about leaking their documents, as we've heard of many crimes committed with others' data. In addition, if someone loses some money, it is not as tragic as understanding that your documents will be used in different casinos. You completely lose hope of playing somewhere and successfully withdrawing your winnings, since each time there is a risk that the casino will accept your account as the one that is already on their site, which means there is fraud.
Sometimes, after making such deposit, before the exchange detects it, you must have traded the Bitcoin to Fiat and withdraw it to your account, so what will the exchange do after you have already withdrawn the money to your account before they later found out that the coins was tainted?
As far as I understand from my short experience, the exchange will not be able to do anything, but your bitcoins will get a mark of their history one way or another. Then it will be quite difficult for you to exchange them anywhere. It should be either with large commission percentages, which is naturally not profitable, or some exchange, where there is always a risk of freezing until the place where you got such "dirty" bitcoins is found out. And of course, you need to show your documents again.