I was thinking about this question over the weekend and I cannot seem to find legitimate reasons why people would want to play at casinos that do not require KYC verification.
1. KYC requirements reduce money laundering.
2. KYC requirements reduce under age gambling.
3. KYC requirements increase the possibility to hold people to account for their actions. (Exploiting casino systems)
4. KYC requirement reduce scamming
5. KYC requirements can be used to restore accounts after it has been hacked. (Using the documents that were used by the original owner)
6. KYC requirements adhere to government regulations and legitimize a casino.
7. KYC requirements can be used to reduce gambling addiction. (Identifying people that self-excluded or people trying to create new accounts)
8. KYC requirements can be used to enforce regional gambling restrictions.
Why would you want to avoid being identified, if you gamble legally and if you are not a criminal? Let's discuss the reasons why KYC are not advantageous for the gamblers and casinos?
Ps. I am playing Devil's advocate... if you did not notice it.

Although we do not have much options when it comes to choosing between KYC and NON-KYC casinos, but one thing which always worries me and it should be a concern for everyone who submitted their KYC documents that what if those KYC documents are misused by the casino ?
Yes, we believe that trusted and well reputed casino will have no such intentions but then the data can be hacked and it may reach to the people with criminals minds. We never know as how much they use that data and what financial damage can be done if that KYC data reaches criminal hands.
Also some people may want to hide this information that they are gambling but when they do KYC then they can be exposed as that data can be reproduced to any leqal entity on demand.