You are mixing Cex, KYC and Dex together. The reason why exchanges are called centralized is because they:
1. They ask you for your information and as a result, you must do KYC(know your customers) as means of identifying the user.
2. They give you a unique wallet address, without the private key and that makes them a custodial organization which are always not safe to use, anything can happen, you don't want them to run off one day right and because they are here doesn't mean its not possible. I want to scare you, read more about the MT Gox exchange.
The Dex is the opposite of what I just highlighted about the centralized exchange. However, DEX and CEX both offer P2P feature where you can sell to any buyer or seller, the difference is that one Cex has act as the middle man that hold the coins while Dex doesn't hold the coins.
I beg to differ with your understanding of a CEX. The first reason for a CEX to be centralized is because it is controlled by a centralized authority. The best example would be Binance which is completely operated by CZ and a few 100 employees. The next example of wallets is irrelevant as there are wallets like trust wallets which are noncustodial but centralized.
The simple difference between a CEX and a DEX is that a centralized exchange has someone or a group controlling its operation. Whereas a DEX is controlled by the users participating in trading on that exchange.
What have you said that I didn't simplify in my explanation or you want me to write an epistle about shitty centralized exchanges over decentralized exchange? Huh!
Centralized exchanges are more than what you think, more like organized crime that package their self as clean people but deep down, they do worse than what you see in the public. Didn't you see SEC and Gary Gensler running after them.
The idea of discouraging KYC is to protect privacy, you don't want your whole life to be monitor just because you want to trade a pair of Bitcoin to shitty usdt, you don't want to your account be lock one day and when you don't have the private key, you are screw as hell. Who do you run to when all this happened? Absolutely nobody and there is nothing you can do about it because it's in their terms and conditions, they could lie against you that you violate one of the terms.
Wherther custodial or noncustodial, learn to hold your private keys in your pant secretly.
Maybe you go through my reply once more, and you will understand we are saying the same thing but in different context.