Sounds great. Isn't Robinhood traders the kind of people who just leave funds on the platform though? Not necessarily the people who buy bitcoin and withdraw them to a non-custodial wallet?
Regardless, even if I don't think it would be used on Robinhood that much, I hope this move pressures exchanges to follow suit.
I mean its hard to measure that accurately, without just being stereotypical. Honestly, I believe any self respecting exchange should require you to transfer the funds to another address that the user owns, I don't like the idea of having a wallet on an exchange, you're just asking for trouble. I'd have an insane amount of respect for any exchange that would build that into the process. Since, that tells me they actually care about the safety of their customers, and not encouraging bad habits. Of course, they won't since the more people they get on their website, the more money they earn since even being on the website probably gives users the temptation to trade.
Same goes for Robinhood, I'd like to see them dropping support for keeping funds on their website, rather than implementing features to better it.
I don't see any centralized exchange ever doing this. Requiring customers to withdraw their coin will lead to higher costs in the form of transaction fees, and will likely result in transaction fees increasing if the exchange is large enough.
Allowing customers to keep their coin on an exchange will also make their account more "sticky" as their customers will have to do more to move their money elsewhere. Further, allowing customers to keep their money on an exchange makes it easier for their customers to trade, which leads to both more liquidity, and to higher trading fees.