Honestly my only problem with KYC is if the process is handed out to some third party I've never heard of before. Seeing these companies that exist just to process my information does not inspire any confidence. Granted I have not fallen victim to identity theft or anything yet so I if it seems as though I can trust the KYC process I would vastly prefer the casino where I win a lot.
There are casinos that process KYC on their end—there are also casinos that store it in their database, so user identities will remain secure as long as the casino has a good reputation and is well-known.
Everyone will choose a casino that often wins, even if they don't care about KYC. Nowadays, even a $5 KYC in an airdrop is common, let alone a big casino win. I think people will chase it anywhere to get that win.