You seem to be expressing frustration with the repetition of certain information. It is indeed unnecessary to mention centralized exchanges separately when discussing the importance of holding your own keys and funds. Since centralized exchanges do not provide you with control over your private keys, it is implied that they fall under the same category as custodial wallets.
In summary, if you are not in possession of your private keys, it is advisable not to store your funds in that particular service, be it a centralized exchange or a custodial wallet. It is worth noting to add with this sentence about hardware wallet that forum users commonly recommend the use it, as this practice is widely recognized and established.
That's why I wrote :
However, every time I read this on the internet, people stop at the Bitcoin storage step. That's not enough. There's another important step: exchanging Bitcoin.
I am not talking about the fact of storing your BTC only, I am more talking about the place where you exchange it