In my own perspective, you should only put your coins on an exchange if you are ready to trade it. Don't put them all if you are after the rewards by staking... It still better to earn rewards by staking using a desktop wallet cause you have control over it.
True that there is an inherent risk in keeping your coins on an exchange. There is also a risk in keeping everything in one private wallet, in case you do something stupid and lose your key.
Personally I prefer to keep my coins distributed in a variety of places, never too much in one location. Of course this introduces another risk, in forgetting what is where.