Never ever trust exchanges to stake. Firstly you will never know if the taking some off the top since there is compounding interest. Secondly, there is the possibility the exchange will run an exit strategy or something happens and they go offline you lose everything. If you do not have the privatekey with you in your wallet then you do not own the coins. The privatekey is with the exchange and you are at their mercy.
There only reason people use exchanges is mostly for staking with masternodes since they are very expensive.
Both, some exchanges do not support particular tokens, or exchanges are just trustless. The majority of my coins is placed on different wallets, but I am also holding stacking coins on exchanges like Binance or Huobi.
What are you talking about? It certainly is not trustless.