Part of education ( some would say a very important part) is meeting people from different backgrounds. The broadest intake is in State Schools. In some areas Secondary catchments are sorted to include children from as wide an economic background as possible. So where I live historically the children come from very poor inner city Primaries and also Primaries in rich areas.
The advantage to both sets of children is palpable. They get to see a life they have not themselves experienced before. Many well paid professional jobs require a knowledge of and insight into the least wealthy eg GPs, Barristers, Teachers, etc.
Many children also have their eyes opened to educational, professional possibilities they'd never heard of before. Win win.
Incidentally it is important that all children have access to free school breakfasts because of the social benefit to include as wide a range of background in none strictly 'learning' situations and to avoid the stigmatisation of just picking out the poorest.
This is why we pay taxes at differing rates so all children can benefit whatever their own parental income etc.