If that uninformed flow is going to market, there is a good market design to encourage price competition among MMs who fight each other for time and price priority. That mechanism is obstructed under payment for flow. Under this, the MM only needs to give at or better than NBBO. The primary competition among MMs here is to pass on as much rents to brokers as possible, instead of minimizing rents in the first place. The market is also more prone to consolidation due to scale economies and informational advantages that private flow access provides.
I also dispute the clean distinction between retail and institutional. Much institutional flow is just funds (e.g pension funds) that hold retail money. If they're getting maximally screwed by this, then so are their investors.