I will tell you what can go wrong, you can send your own identity for verification, and they can be unaccepted for undisclosed reason. Many years ago, I have sent documents to receive tokens, but they were rejected. It was simply written "failed passing KYC". The project gave only one attempt to pass it, and they never explain why and where I have failed. Same thing can happen anywhere and with anyone. User can simply get failed to pass nobody would bother giving any explanation; sometimes they dont even have to explain anything at all. Just fail and bye-bye.
Well, maybe only in that way will gamblers really leave because they have no other way. Because usually, gamblers only have a way to use VPN for restricted areas about gambling, but when a gambling site or platform implements KYC requirements, users who previously used VPN may also be affected. Because after all, when previously they could log in with VPN but because their area has been revealed from the identity obtained, then in the end the related user will be restricted from using the gambling site. But with that, it is at least a reason for us to choose to remain anonymous because by doing so, users will remain comfortable and safe from existing restrictions.
some websites block VPNs but you are correct, sometimes all you have to do is use it
but if a gambler don't intend to KYC they should probably be playing on a different playground than risking a big win not getting paid because they didn't send their documents
better to avoid the issue from the beggining.