I will share my own experience. Binance freezes my funds when I receive funds from my clients. Because one of my clients sent BNB from a mixer. However, eventually Binance returned my funds but restricted my account, so I can't use Binance anymore.
The second story was learnt from the scam accusations board. Bybit asking him for transaction details with videos of where he got the funds. That user also used a mixer to send funds to Bybit 5 years ago. So Bybit is asking for proof source of funds, which is impossible.
Many warnings about this risk of storing fund on centralized exchanges or receiving your payments directly into your centralized exchange account.
Events made you scare about custodial wallets, centralized exchanges..I really don't know that Bybit or other centralized exchanges go too far like 5 years ago to check mixing-related deposits of users, and ask them for proof of fund. This story can be true or just fake, I can not verify it, but I note it as one of information about risk of CEX.
So what we learn is that funds shouldn't be deposited to a centralised exchange directly from any third party. You should bring the funds into your non-custodial wallet first. Then you should use CEX to buy crypto coins and move them again to a non-custodial wallet. In the meantime, if the exchange is about the source of funds, you can show them with video proof, etc.
I agree with you.
Receiving payments in your non custodial wallets, and if you are careful and can afford to pay transaction fees, you can move it to one or two more wallets (non custodial wallets of yours), before sending it to your CEX account.
Bitcoin Q&A: Blacklists, Taint, and Wallet Fingerprinting. This video is 5 year old and maybe many things changed on CEX policies on tainted coins and wallet fingerprinting.