Yes, unless it's a minimum million dollar case, the police won't waste time investigating them. So kyc for gambling, holding or trading with low amount should not be a fear for you. But one fear is that many casino sites sell users' documents on the black market to perform illegal activities, so you have to be careful about this. And for this reason, a reputable casino site should be used so that you can be safe from all aspects. Illegal operators buy documents from users for high fees that many sites cannot afford and sell the documents to them. So it is better to use reputable sites
I doubt with casino reputation will sell their user document on the back market illegal activities because they won't loss their reputation have build hard by selling data without much valuable, in my country have many time data publishing and selling in the black market due some of government side exactly take down by the hacker and not really huge impact when your data publishing or selling. Some casino have good protect with document user and not easily will publish exactly sell to black market forum, its impossible with any trusted casino have been publishing with their user document. Don't really afraid if want be part of casino user you have allow with the rule or term of service casino require with KYC.