don't keep them on the exchange unless you want to sell.... they won't stake over there...
Well, they will stake over there, but the exchange will probably take the profit for themselves...
You could imagine an exchange which shared its profits from staking customer coins with the customers to give them a competitive advantage - "sell your clams on our exchange and we'll share their staking profits with you until they sell".
C-CEX ( not my favorite for sure BUT.... ) actually does split the stake up amongst ENRG coin holders when ENRG stakes...
The only ones that do as far as I know...