> Think of Robinhood and how they gave users more expensive trades because they were paid for routing flow.

That's the opposite of reality. Most trades are cheaper routed to a PFOF market maker because they know it's just retail trades. Uncorrelated "dumb money" that isn't going to be steamrolling them with a $10m sale.

Also that would be obviously illegal and the SEC would jump down their throat. Brokers must give clients best execution.