Robinhood isn't allowed to use your money as collateral with DTCC, they must use their own. That's why it doesn't matter what kind of account you have.
Presumably their lack of trade fees hurts them here.
That does not seem right unless there is something more hidden going on:
1) I issue on order and close a trade (using a broker as intermediary)
2) i have already provided the liquidity to settle that trade which is already in the broker's control
3) why would the broker need to provide more liquidity to guarantee this trade?
I have the feeling what you say is true but only because there is some finance magic going on that nobody needs but the finance system.
I have tried to look for more information about this DTCC requeriment but couldn't find much.
Presumably their lack of trade fees hurts them here.