So the only viable solution to this is that a person finds a casino that is reputable and trusted and only gamble with them so that if they are asked for KYC verification, they don't feel hesitant to do it knowing the casino is trusted and they can give their documents to them and they will be safe, somehow.
It's another matter if you're required to submit your information in compliance with the KYC requirement and you have doubts about whether the gambling site can truly safeguard your private documents. If you have trust issues with crypto casinos, then choosing a fiat casino can provide a sense of security, as you can be sure they are regulated right from the start.
The difference between crypto casinos and fiat casinos is that crypto casinos advertise anonymous gambling, at least in the early stages. However, as government regulations tighten, they gradually become more like fiat casinos.