Well you can't blame gambling sites nowadays to add KYC since gambling sites now accepts different crytos and allows you to exchange example BTC to ETH. If its a new site and ask for KYC, I wouldn't try to send anything to them, but if its an old site that has been running or operating for several years already, I would go for KYC.
Just because a site has been in operation for 3-4 years, there is no guarantee that they can be trusted. Because the ownership of these casinos change very frequently, and if someone is able to purchase a well reputed and long running gambling site, there is no surety that he is very clean. With the amount of identity forging going on these days, I would treat KYC as a last resort. And I am definitely against doing KYC in any of the gambling sites, no matter how reputed they are.
You just dont want KYC for reasons best known to you because if you truly desire to drop your KYC you will understand that a reputable site that have been in operation for years will not compromise its standard for any reason. KYC regulation is just a way to have details of a clients and no reputable site would do anything bad with it.
If your fear is what if the reputable company sells over to a new management entirely, well I feel a reputable company would hand over to someone they can trust , because theyve already successfully built a brand name and they will not allow it go on the mud for any reason.