To be honest, I don't think there's much problem if you'll try other gambling platform as long as you think that those are reputable enough. I've been with multiple gambling platform and tried to gamble on some of them however I never tried to do any KYC to avoid any future conflict. Still, staying on just a few casinos is one of the best choices rather than sticking with multiple casinos.
Knowing the consequences of your actions is very important, with KYC information, you can easily be traced by the authorities or your data can be sold on the black market if the casino is not reputable, so at least know the risk. Actually, there are plenty of reputable casinos that do not require a KYC, not totally they won't but only when you pass the criteria, but for small-time gamblers, there should be no problem as we are only dealing with small amounts of money.
It is risky to trust a casino and get verified with personal documents because of the mentioned reasons. From the perspective of casino management, they have no choice except "Know Your Customer" and ask the proof about the source of funds. Like crypto exchanges reputable casinos can also be hacked, reliable casinos usually store documents on separate servers to protect customers. If the user is not sure about the passing KYC 2 level, he should seriously think about alternative anonymous casinos to continue gambling.