Why would you want to avoid being identified, if you gamble legally and if you are not a criminal? Let's discuss the reasons why KYC are not advantageous for the gamblers and casinos?
Privacy.
And also avoiding your personal data and government documents falling into the wrong hands. Any centralized exchange can be hacked, just like Poloniex demonstrated. And so can a DEX. But with a CEX, the problem is that they have files which could be used against you, for example identity theft, and after that comes much worse. I would not recommend it. Imagine waking up one day to discover you are a wanted felon in some foreign country and you owe people money because someone borrowed money with your ID. Really bad situation.
If you absolutely need to trade, use a good DEX.