As someone who has looked into but not actively used Robinhood - the main benefit of the Gold subscription is for day traders. With a free account, if I decide I want to sell AAPL and buy GOOG, I have to wait 3+ days before I get the money from selling AAPL credited to my account. With Gold, they basically let you float, so you can immediately get into a new position after getting out of the previous one, without having to wait for your previous position to settle.
I believe that is far and away the primary use case for Gold.