Most of crypto sportsbook don't need KYC process but it will needed IF your account looks suspicious by the site such different IP, location, multiple accounts or winning big (for some sites). If it needed, usually are your ID, Utility Bill, bank statement, take a photo you with your ID and else.
Gambling sites have their own reasons why to ask for KYC, and like what you have said, those reasons from the list mostly happened especially when your account have suspicious movements inside the house. You need to process this procedure as it will give more access to that specific gambling house after passing the required identification.
For those who are just playing little and there's no problem with the account, they can enjoy using the house without any issues.
True, small gambler usually can gamble without problem at all, easy and fast withdrawal but when it comes to big bettors the house usually check it first like if you withdrawal 5 bitcoins, of course the site will check the account first. Actually i heard so many times a case where that once you won big and withdraw, some sites will ask you to verify KYC.