In 2021, it's very hard to detect a transaction from a centralized mixing service like ChipMixer or such good reputed services.
This is incorrect. Each year more and more companies track transactions at blockchain and each year they get more resources from KYC exchanges. Being 2021 does not make it harder to detect. It makes it easier.
However, i think about Chipmixer who has the only mixing kind service as the user will receive private keys to spend from instead of a direct transaction to his wallet. Would they be able to trace it also ?
It does not protect you from mixer detection.
Receiving private key protects you from timing deposit and withdrawal. For example - you deposit 1 mBTC now and you receive 1 mBTC chip created week ago. If you spend it right now attacker may guess you are one of ChipMixers customers who deposited 1 mBTC between now and week ago. If you spend it after month then amount of customers and possibilities grow.
In the worst cases, if exchanges as well as governments are able to track a transaction to know it's coming from a mixer, mixing in general will be useless.
This is incorrect. Mixing protects your privacy as in how much you have and how you spend it.
Mask protects your health. If anyone can detect you using mask - is it useless? If shopkeeper forbids you to enter with mask - will you hide it or will you find different shop?
KYC exchanges will block your Bitcoins. Because you mixed them. Because you gambled. Because you received them from different country. Because you used Wasabi wallet or other forbidden software or service. Because you do not have full name and address of a person who paid you.