Do you mean middle income, rather than those who own their means of production? Because I'd say the parents of those I see attending DC's grammar have to work for a living, so doesn't that make them working class?
Our comp of choice has a lot more parents who own their means of production, but there are only a few talent-based places and then nothing is guaranteed unless you live within about 300 yards. The grammar is completely without catchment, and the parents far more working class than the comp. Uniform is a bore, but we managed with sale stuff at induction, with the creativity expected of anyone capable of gaining a place. At least three-quarters of the intake is not the Emma/Annabella/Cosima type you describe, perhaps they couldn't make it even with tutoring? Teaching is professional and pastoral care is fantastic, as is in the comp we missed getting into. The travel is a real drag, but the intellectual company miles better than the public school other DC attends.
If the economic dregs of society such as we do not complain about school choice, why should you presume to drag us out of our circumstances? People like us live with what we can make of our lives. It's often the middle income types who complain about what someone else has that they cannot get. We're fine with the social and community ghettos we inhabit, thank you.
As for banning higher income families, they also love their children, don't they? They also know you cannot choose academic ability at birth. They have to pass the exams. There is no correlation of note between economic standing and gracious behaviour. We apply for schools because we think we'll fit in. Being poorer than everyone else is neither here nor there, unless they're poo bottoms anyway. And nobody over the mental age of 14 is bothered by those.
I'd be far more convinced if catchments were completely removed from academically selective schools. That may reduce ghetto formation of the more economically agile. The demand for tutoring must be good for the country, surely, with everything else being rationed?