Personally I always move anything I buy or earn into a wallet where I retain the private keys It provides me peace of mind. Bitcoin is strong but with that power comes responsibility and a key part of that is privacy and knowing the present regulatory landscape
I am wondering if a person buys his Bitcoin in a centralized exchange, and sends it to his wallet directly, how can he say that he protected his identity? Isn't it as clear as day that anyone can track a person's identity if he bought his Bitcoin in a centralized exchange? While in a decentralized exchange, those who deposit fiat still use a third-party provider in order to buy Bitcoin and these third-party providers still ask for KYC, thus they can still trace the person's identity through this third-party provider.
I think the best way to protect one's identity is to buy Bitcoin face to face even though it has risks.
It is indeed very important that we store our Bitcoin in our non-custodial wallet in order to have full access to our Bitcoin anytime.