I never thought about it, but that would a win-win for them. They can keep a percentage of the reward as a fee for staking but more importantly, they retain that investor's liquidity. When someone stakes in their own wallet and decides to send the coins to an exchange, they have many choices of where to send. If they were staking on Coinbase, they'll obviously keep their funds there for trading.
They've already got a lock on the fiat gateway market. With their new approach to altcoins, it seems like they saw how much of their customer base withdrew to Poloniex, Bittrex and Binance in the 2017 bubble and they want a piece of that market. They want to be a one-stop shop for casual investors. Staking for a fee fits the scheme well.