To have top scale protection on your assets you should be keeping them on a private wallet so you don’t get swept away by unexpected losses when you have them on an exchange.
But for the OP it’s about trading not funds protection or security. The OP is recommending trading not only on one exchange and there is sense in that.
By unexpected losses do you mean theft attempt or hacks from a third party? If yes, you are right. As a trader, only have money for trade in the exchange and by the time you are done trading you send them back to your wallet.
I know many persons would complain about the fees during these process. Since spending fees every time you end trading, you can do it weekly, at the end of each week you send the profits to the wallet and leave only the amount you want to trade with.