It seems like this "if you are not holding the private key then, the coins does not belong to you". We can't blame people who doubted now with some exchanges, even though they are look likes legit now. Because recently we have crypto exchanges that victims of hacking and exit scam by the owner. I did not say in generalized but that was the point of view now from crypto trader. However, trading is still profitable.
As a trader, you wont really have any choice but to deal that kind of risk on where putting up funds into exchangers which you do know that you dont possess the keys of its wallet
I fully agree with this point
If you want to trade actively, you have to keep a stash of coins in an exchange account. But there are ways to minimize this risk even if it is next to impossible to get rid of it altogether (other than using decentralized exchanges which come with their own can of worms and a host of other problems)
For example, on exchanges that allow margin trading (think Bitfinex here), you can open margin positions being only partially covered by your exchange balance with the bulk of your wealth still sitting in your desktop wallet. Thereby you decrease risks associated with keeping your money on exchange (as you don't have to keep all your coins there)