The "certain regulation" here is simply that you can't advertise to your customers that you're getting them the best possible deal when you have deliberately chosen not to give them the best deal. As the SEC points out: their pricing isn't better than traditional brokerages. This isn't like Uber, where the lie is that the low prices are subsidized by investors and will be jacked up later on down the road; here, the lie is taken directly out of the hide of RH customers.

That's true only if the service Robinhood is providing is giving customers good deals. It seems quite plausible that instead it is actually providing entertainment in the form of "free" trading. If this is the case, the lack of explicit commission is a key feature.