Robinhood has stated that they will be setting up Crypto deposits and withdrawals in the future. They even tweeted about it as if it was going to happen soon, but then nothing after that. It was just enough press to get people off of their backs. To be honest, with everything that is coming out about them I would not be surprised if they were taking the coin that was purchased for the company and putting it in one of the interest baring exchanges and then keeping any earnings (personal speculation, do not take this as fact).

That being said, I can see the benefit of a system like Robinhood's for investors that do not want to actually deal with keeping the keys. But, that can be done with most of the Exchanges out there and you get to keep any staking or interest.