You can't really expect privacy if you are using centralized exchanges. Most of them require that you undergo KYC, so they will know who you are. no matter how many routes your crypto takes before getting from your private wallet to the exchange wallet, if the exchange knows you are John Smith, they will know it's John Smith's coins that were just deposited in his account. CEXs also co-operate with chain analysis companies to de-anonymize their customers.
The word privacy has no means when you are using CEX for your funds as we have seen top exchanges doing the cheap tricks and playing with the personal data of users for their personal benefits and this is fact we are aware of like :
1) Coinbase restriction of $1000 CAD to reveal the indentity of recipient and then additional information also
2) Coinbase selling users data to some third party companies with mailing list that are then prone to hacks.
3) Binance selling data to Russian government and many more things we are aware of .
The part is you don't own keys to your funds and they know you are John smith but the funds are actually of the exchange and they can put some restrictions on your easily like the bank accounts.So avoid using these CEX for fund transfer.
Afaik Kucoin doesn't ask for KYC so it is still possible to deposit/trade/withdraw crypto from there without revealing your identity. I have an account there since 2017 and so far they didn't ask me for KYC (I use it very rarely though and never with bigger amounts). With that being said, I still wouldn't use them for larger amounts of money if staying anonymous is priority as just because they usually don't ask for KYC it doesn't mean they won't if you try to withdraw bigger amounts.
Yes if you are small investors then you can use Kucoin for trading purpose as you can deposit funds without going through KYC process and also withdraw easily as there is limit of 2 bitcoin per day without KYC and can increase to 100 or more with verification completed.But if you are long term holder then hardware wallets are the best option without any hindrance.
KuCoin users that complete KYC verification will enjoy higher daily withdrawal limits. The new withdrawal limits are listed below.
Verified Individual Account: 100 BTC per 24hr
Verified Institutional Account: 500 BTC per 24hr
Non-verified Account: 2 BTC per 24hr
Source So the best is to avoid them if possible..