Is important to carry out all bitcoin transactions through your own wallets

[Mpamaegbu]

To be on the safer side and not lose your bitcoin, because of regulatory compliances, from a centralized exchange wallet, it is better you first receive any bitcoin payment into your wallet, that you control with your private key/wallet seed phrase saved and can restore the wallet anytime.

Nobody should fault what you said in the upper part of your post concerning sending Bitcoin first to one's wallet instead of directly to an exchange. It saves the hodler any unnecessary updated terms and conditions of centralized exchanges we can't run away from. However, we ought to also know that part of the advantages of Cexs is the ease of regaining access to one's account if password is lost or forgotten. This isn't the case with private key or seedphrase of private wallets. Once those are lost, they're lost forever.

[collecttmaster]

To be on the safer side and not lose your bitcoin, because of regulatory compliances, from a centralized exchange wallet, it is better you first receive any bitcoin payment into your wallet, that you control with your private key/wallet seed phrase saved and can restore the wallet anytime.

Nobody should fault what you said in the upper part of your post concerning sending Bitcoin first to one's wallet instead of directly to an exchange. It saves the hodler any unnecessary updated terms and conditions of centralized exchanges we can't run away from. However, we ought to also know that part of the advantages of Cexs is the ease of regaining access to one's account if password is lost or forgotten. This isn't the case with private key or seedphrase of private wallets. Once those are lost, they're lost forever.

The last comparison is wrong and is not a benefit of CEX. You just picked very specific situations to make a bad comparison. If your CEX account is hacked your funds are lost even if you recover it later, that does not help you. It is the same with private keys. Any responsible adult will not lose neither of these 2 things.

[Findingnemo]

No it's not safe to receive mixed coins to your wallet and send them back to an exchange or casino because they use service which tracks the trail to certain number of cycle and if they flag something that's coming from layer 5 still the exchange can hold the account and asking for the source of the funds.

If you want to use mixed coins then check the AML scores first and it's better don't use centralized platform to deposit mixed coins, better use with any decentralised exchange.

[khaled0111]

However, we ought to also know that part of the advantages of Cexs is the ease of regaining access to one's account if password is lost or forgotten. This isn't the case with private key or seedphrase of private wallets. Once those are lost, they're lost forever.

I don’t think the topic is about which one is safer, personal wallet or CEX. It’s about the importance of sending coins from your personal wallet to a CEX rather than sending it from another custodial service.
I can think of two scenarios where this can help: In some cases and for different reasons a centralized exchange may ask you to provide a screenshot of the wallet from which you sent the coins (proof of ownership) and this happened before.
Another case is when something goes wrong and the exchange decides to refund the coins to the address from which they were originally sent.