(None of this makes Robinhood good; it's just that PFOF doesn't explain why they're bad).
> the cost basis of trading with you is lower than with trading with the broader market
But this is exactly why Robinhood is bad. Trading with you (a retail investor) has a lower cost basis because retail investors are reliably less sophisticated than institutional investors. Therefore: an institution will pay to take the other side of a series of trades with you because it knows you aren't sophisticated, so it's likely to win in the long run.
From there, follow the incentives: Robinhood is incentivized to sell more order flow; which it does by increasing its trading volume; which it does by making trades easier. Robinhood is also incentivized to increase its net revenue per trade; which it does by increasing the price at which it can sell a given volume of order flow to institutions; which it does by making its average trade less sophisticated.
In summary: The most obvious way for Robinhood to optimize its revenue is to get its investors to make lots of bad trades.
The money they're making is just the spread. They can safely quote better spreads to retail investors than they can to execution firms trading for giant funds.
That concern might exist because I'm selling a big position and my order is the tip of that iceberg, as you say; but it could also exist because I'm trading on news that hasn't yet been incorporated into the share price, and my order will be followed by many other people selling once they learn that news themselves.
It's not about winning or losing, it's about getting "run over" by massive momentum. Retail investors move less volume and randomly take both sides of trades, so it's much less risky to trade with them. Conversely, large players can dump so much volume that they move the price against a market maker and decimate their revenue from whatever very small spread they usually collect.
> The most obvious way for Robinhood to optimize its revenue is to get its investors to make lots of bad trades.
Robinhood doesn't care whether trades are good or bad. A discount brokerage is a moving business, not a storage business (unless you count interest on cash balances, which Robinhood doesn't make much from). They make money from retail investors doing a lot of trades. Arguably that's against the interest of the investors because retail investors tend to make bad trades, but there's no malice on the part of Robinhood there. If all their clients made a lot of money presumably they'd use it to make more trades and make Robinhood more money.
So, let's say you are trading 1000 shares. Normally, you might pay around $10 for that with a real broker. Now you execute that same trade at RH (or some other zero-commission broker), and let's say your average price is just 2c worse than what the other broker would get you. Well, now you just paid $20 for your "free" trade. And this gets worse for odd-lot orders (those that are not multiples of 100 shares). Because with those the MM is not bound to the NBBO, and can give you an even worse fill. Given that a lot of these RH accounts are presumably rather small, that likely applies to a decent amount of orders executed.
> the cost basis of trading with you is lower than with trading with the broader market
These are market makers; they don't take directional bets, hence this is irrelevant, as they only trade in a reactive way while trying to maintain a neutral book. What you are presumably talking about is toxic (i.e. informed) vs non-toxic order flow. Having a big player, who knows more than the MM, is what they are afraid off, because they can lose a lot of money by being on the wrong side of the market. They know that retail traders are unlikely to be informed traders, hence their order flow is less risky. However, the volume retail traders are moving is a drop in the bucket compared to what instis do.
I'd love to know how that split gets decided. I guess it's "as much as possible to the brokerage without looking so lopsided that someone writes an article about it", except at brokerages like IB that publish data on execution quality and try to market based on that? Do the contracts between the brokerages and the market makers specify the quality of execution in any detail, or is that just a long-term reputational thing?