I agree, but the problem is finding a trusted person, especially when it comes to larger amounts - no one should walk with thousands of $ in their pocket, and also not have a larger amount of BTC in some hot wallet on a smartphone.
If you use a platform such as Bisq or LocalCryptos, then you will deposit the crypto in question to a non-custodial escrow before meeting your trading partner, so you are not carrying the crypto in a hot wallet. Similarly, you could always meet at a bank (or even an ATM depending on your country's daily ATM limits) and take cash out immediately prior to the trade. I've done this before, and it also removes the risk of counterfeit cash being used.
That way you will remove the trace to your coin and you are accumulating Bitcoin anonymously since on your method
There is nothing anonymous about using a centralized exchange. Sure, if you pass your coins through ChipMixer then the exchange will not be able to see where they end up, what you spend them on, who you send them to, etc., but they will still have a complete record of every single satoshi you have bought, when you bought it, how much you paid for it, and when you withdrew it, and they will link all that against your real name and identity and share it with who knows how many third parties or government agencies.