This is for the newbies to Bitcoin and bitcointalk at large, urging you to take your privacy and compliance seriously, since regulations from various governments are beginning to take interest in Bitcoin transactions, and just as the phrase goes. (Not your keys, not your coins), knowing that makes you stay guided on how you handle your Bitcoin transactions to avoid losing your assets to AML and other compliances.
Note: there are some red spots that regulations state for coin receptions, such as Bitcoin mixers and a few gambling sites, although the majority of the centralized regulated Bitcoin wallet hosters like exchange high restrictions on deposits from Bitcoin mixers, whereas are linen on gambling deposits.
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.
Bitcoin global payment is taking shape, and a lot of services are now paid using Bitcoin, and at that, we have to take the security of our Bitcoin seriously, by making sure that we are the custodial of our Bitcoin before anything.
With lots of hacking that is happening in centralized exchange, and also with the recent hacked happen in Iran, meaning putting profits and funds with large amount is not safe, OP is right having control with keys and seed phrase, is the best thing we can do, imagine you have 100 bitcoin in an exchange and gets hacked, what if the exchange has been hit by a massive hacking that they can't recover that would been a disaster for us users.