I am sure that is the reason for the most gambler who doesn't play gambling too often. They will prefer to choose the gambling website, which doesn't require KYC because they don't think that it will be safe for them to give the personal document. I don't like to verify myself just to playing gambling, and I don't see any reason for me to do that thing because I only want to get fun in the gambling games.
That's it, and gambling sites do understands that, even exchange like Binance which is one of the most popular exchange in the space is not so strict with KYC.
They allow traders to use their platform without KYC up to a certain limit or condition, because they see the possibility that they would loss clients if they will be very strict, same with gambling site of course, less complicated will give more comfort to gamblers and they will choose a gambling sites that gives them that comfort, people does not care much about the license of the gambling operators, they cares more on the reputation.