Honestly, I believe any self respecting exchange should require you to transfer the funds to another address that the user owns, I don't like the idea of having a wallet on an exchange, you're just asking for trouble.
Even better, use a DEX like Bisq which means your coins are never stored on their platform at all, and go from your wallet, to multi-sig escrow between you and your trading partner, to their wallet, or vice versa.
Good point. See, to me an exchange which did that would have much more credibility than any other service out there that didn't, and to be honest credibility, and therefore trust should be at the top of their agenda. Although, obviously profits cloud their judgement, but I'll be quite honest I care far less about how well an exchange is doing, than user security. Something which exchanges should be caring about, but the truth of the matter is they don't, they only care whether they're storing that Bitcoin on their platform. They likely do measure the amount of Bitcoin stored on their platform, and they likely have internal meetings about how they can improve/increase the amount stored on their platform, as it probably directly correlates with profit.