They can't stake that ETH because their users may want to pull it out. Staking it means that you make it unavailable for use, and if you try to break the rules while staking you lose it.
They could probably stake some of it though, as long as there's no bank run situation.

If there was even a hint that Coinbase was pulling any "fractional reserve" stunts, they'd lose the massive amount of credibility they have over less reputable exchanges. Reputation is the primary advantage Coinbase has.