If my Robinhood trades of 100 lots or more execute at a few pennies higher than the price when I place the order, I think that is entirely fine. Why? Because it costs 5-10 to trade from Etrade or most other normal brokerage accounts. From what I've seen thusfar (I've got maybe 20k invested with RH), all of the trades have executed at the price I expected them to, or 1 cent higher on very volatile stocks (TSLA in specific). I'm still paying massively less than if I used a traditional broker and RH is making a bit of money by selling my order flow.
Win/win really.
They're not really allowed to do that and I don't think they are doing that. Robinhood (or whatever wholesaler they route your order too) is required to execute your order within the nbbo. They can't just e.g. fill your buy orders a few cents above the national best offer because they want to make some extra money. The regulations don't work that way...
[1] https://en.wikipedia.org/wiki/THOR_(trading_platform)
[2] http://www.nanex.net/aqck2/HowSlowIsTheNBBO_%20A_Comparison_...
I've written a fair bit of code (python) to parse my statements and make sure things true up with what personal capital says. The app thing is annoying, but RH just closed 110M and they'll get more functionality in the future. You're not the first person to ask that and I figure eventually they'll have to open things up or they'll lose customers (like me). Right now, I'm ok with using it for a year or two provided they allow me to continue no-fee trades.
Are the tools actually good? Several low-cost robos (Wealthfront and Betterment) now have fairly good retirement planning interfaces which take your outside accounts into consideration and Mint has investment tracking now as well.
I can see the benefit in making it easier for people to get access to things that are often hidden behind layer of complexity and "need an in", but I can also see the perversity of building a business where your money making system is "put debt on people who don't quite know what they're getting into". The point is not that they allow it, it's that they have a direct incentive to make it happen as much as possible.