I believe this is being followed for the purpose of making everything transparent and not to get into illegal things. If thats the case then these exchanges shouldn't accept funds from gambling sites.
They have their own rules and it's up to them how they implement them, gambling sites are ok accepting depositing, but they will give you issues when you try to withdraw your winnings if they don't want anything to do with a gambling site, you are right that they should not accept withdrawal and deposit from and to a gambling site.
^ No, I disagree, that is not how trusted gambling sites work even they implement KYC verification to their users. It is a matter of the government law that under their license. User will not be reading the terms and condition will most likely fall into this issue and they will have a problem upon withdrawal in the future. Nevertheless, we should always be careful transferring fund to the centralized services, even on my country, we have a local wallet here that don't accept cryptocurrency that comes from gambling, once they will verify it, your account will ban and it will not open anymore altogether with your fund.