They can't check everything (all coin history). They would block a lot of people who doenst even know what mixers are , and probably even block coins that came from another cex. Mixers exist for a long time and the amount of coins whi has ever been in casinos or mixers is enormous.
I've worked in the Risk department of a CEX, and all transactions were analyzed by an AML/CTF algo. On the other hand, it's a set of factors more than the transaction itself that can lead to the transaction being frozen. Each user has a Risk Score based on the frequency of deposits/withdrawals, the amounts, the origin of deposits, their country of residence, and the SoF questionnaire they filled in on registration (income, expected volumes on the platform, etc.). Clearly, coins with a history with a casino or mixer aren't a problem if they're the user's only red flag, but if other flags are present, they'll use this as a pretext to justify asking for the origin of the funds.