Unfortunately, there is nothing we can do about and we can not even know if the casino is asking for kyc for actual security reasons or just to scam. You will have to trust them.
In God we trust, in others time will tell. Fortunately, if a casino has a good reputation, it is what we can trust based on their history. Note that it can be changed in future.
This is why I personally prefer when the casino impose kyc from the beginning when you create an account or before you make your first deposit rather than to wait till you make a big win or they suspect your activity.
When you register on a licensed casino, you should be prepared to get asked to submit your documents at any moment.
It is same to register and start using a centralized exchange. If you are seriously to use that exchange and intend to put big capital there, you should complete KYC even it is not mandatory before start using it.
Exchanges have rules to ask KYC if they detect suspicious things like IP address changes when log in, huge withdrawal request, strange trading with your account. The first two reasons are most common and honestly, I don't want to have problems if my KYC is failed and I have huge capital in that account.