Yes, the centralized exchanges also have their part in bringing this non-KYC services down. They would like that people go to the eXch and get their funds exchanged without any hassle. Those exchanges would ideally want that people uses exchanges to convert their coins and they have the KYC which they use as a weapon to enforce government authorities to get down such services that are operating without any KYC. Exchanges like Coinbase, Kraken, Binance and others etc that operate under strict government regulations can also attack the non-KYC exchanges by blocking Blocking Withdrawals to Privacy Wallets like Wasabi or Samourai. They may Flagging Non-KYC Transactions when you transfer money from CEX to non-KYC exchange and many other tactics.
That's correct, but in my opinion, it is even worse than that because centralized exchanges try to over-comply with regulations, going much further than any other kind of financial institution by tracking what you do with your bitcoins AFTER you withdraw from them. If they see that you participate in a CoinJoin with bitcoins that you withdrew from them, they request additional information from you under threat of closing your account, which in some cases means they take the money in your account if they don't like your explanations; what creates an incentive to request more information.