Do you think there are no reputable casinos where KYC is not required?
One of the most important and fundamental features of cryptocurrencies is anonymity. In my opinion, cryptocurrency casinos should not require KYC verification. Of course, if you prefer to undergo verification, please, you can do it anytime and anywhere, but in my opinion, if someone plays cryptocurrencies and does not want to undergo verification, should have such a choice.
And there are reputable casinos which kyc are not mandatory, some will automatically ask you for kyc when you exceed on their given free limit.
In most casinos there is no information that there is a limit. Usually, it is written in the rules that they can ask you for KYC verification at any time.
How does he know that a reputable site will take care of his kyc? Did he try working on that specific field already? Facebook is also reputable but there are reports that Facebook sells the data of its users.
We don't know maybe the same thing are already happening in the background when we submit our kyc on our favorite crypto gambling sites. We have no idea because no one have ever exposed it yet. It's not only about if our kyc is safe or not but it is also about privacy. Some prefers to be anonymous.
This is a separate problem. Personal data is a completely normal product these days. Whole databases are available on the Internet, sometimes even for free. We will never be sure that our casino details are safe. This is another argument for looking for an anonymous casino just like OP is doing.
most of the casinos that require KYC have limits like if your deposit/withdrawals exceed 2k usd or 2k euro, depending on where the casino's area of jurisdiction. but yes, some won't publish their limits. in that case, if you are worried about kyc, try to contact their support what max amount you can depo/withdrawal without worrying their kyc. if you are abiding their protocols, you won't get any trouble, unless you win big, and the casino may possibly look at your account and start asking kyc before they release the winnings, which usually happens if the casino don't have much bankroll.