The thing is a lot people have this misconception that "No Kyc" means a lifetime pass when it actually means "No Kyc at registration". Most of these gambling sites have security software running in the background at all time so when you try to engage in anything that it's strange to them, they automatically ask that you provide your ID, sometimes, you're required to do so even in small transactions.
This misconception can be corrected in first place if they put correct information towards that their KYC rules. If they just put that No KYC thing on their header, many people will just immediately assume that their casino is not implementing that requirements.
That's why its kinda misleading to put that word, while in fact they are writing about possible requirement if they request a user to undergo with this process.
With those cases happen and many cases hide this information's, its really better for people to read the TOS to avoid having those unwanted KYC surprises.