You’re right. Use a centralized exchange (CEX), and you’ll be KYCed and de-anonymized. That’s why most privacy-coin users prefer DEX. For normal persons, if privacy is important, using anonymous gift cards or prepaid credit cards, which you can easily buy without ID, is more practical, much better than KYC'ed crypto.
If you can somehow get KYC-free coin, maybe from DEX, i.e. if you can get it personally from your friend or peer without showing ID etc., then and only then, you have real private crypto. There are two popular ways for this (Bisq and LocalMonero). Another option called Haveno is hopefully usable soon, but that is still iffy.
Using DEX is not essentially difficult, much safer than you might imagine due to a mechanism called multisig, but maybe this option is not for normal people. When you feel experimental, you might want to try to buy a small amount via DEX, to see what it’s like. If you’re a popular programmer or artist, accepting donations in crypto is also an easy way to get no-KYC coin. Another option is p2pooling—you can get a few Euro worth of XMR relatively easily; yet this last option is time-consuming and not very effective. Many of p2pool users or full-node people are privacy-advocating volunteers, maintaining/participating the Monero network for philosophical reasons, fully aware it’s not profitable in terms of money. This might be part of the reason why Monero tx fees are almost zero (like 1/100 of that of BTC). At the same time, there are many sketchy people around crypto too 😟 Be careful and stay safe!