Yes, we believe that's how it should be used - no KYC required for lower, 'recreational' stakes. But KYC for large amounts where the possibility of money laundering becomes relevant. This system is what we will be implementing when we launch exbet.io later in 2019.
But I think if you want to use KYC, it should apply for the gamblers who will be using a big money to playing gambling. I am sure that you can see it in the each member's history so you can send them an email or message telling them about completing the KYC. But for gamblers who will not use a big money, then they don't have to complete the KYC because they only use small money to gamble and who knows, they are gamble for just fun. I think that will prevent the money laundering that you worried and the gamblers will be carefully to use a big money to gamble. That is the only suggestion for you.