KYC is definitely not a problem on a trusted classino site in this case coinplay has become very trusted and popular these days so I don't think kyc is a big problem here either. Coinplay has now started their marketing more actively and is trying hard to establish themselves as a major casino platform and they are quite successful. I have been using Coinplay for a few weeks now by completing kyc and feel very comfortable here.
Problems can be big or small.
On trusted platforms, it is a smaller problem as at least they are not scammers and they won't require you to do KYC in order to steal your personal documents and at the end steal your money by reject your KYC submission. However it is still a problem because you never know how your documents will be secured, hacked, leaked in future. Again, you have to trust that platform security that can protect their data base including your documents.
On new platforms, it is a bigger problem as it's unknown that will they vanish to the air with your document and money. Other risks are as same as above description.