I don't disagree with you.
My preferred solution would be to have non-selective intake schools with setting for all "academic" subjects. This would require larger schools than is currently the norm, at least 300 students per year with at least a dozen classes for the subjects that all, or nearly all, students take (double these numbers would be better). That would allow more than one top set and more than one bottom set in the most popular subjects to facilitate timetabling. Students would be able to change sets at least every year, if not every term, with some provision to help the ones moving up a set, even if only a folder of additional worksheets to be done over the term breaks.
A school organized along these lines would provide some of the more homogeneous classrooms which make teaching easier. It would allow students to work at faster paces in some subjects and slower paces in others, as most appropriate for them. It would allow a more "diverse" student body, in academic achievement as well as family background than a selective school.
Schools like this would not eliminate the inequality in the system, perhaps not even reduce it. I have every confidence that the most academically ambitious and well resourced parents will continue to cluster around the perceived "best" schools, and that schools in poorer neighborhoods will, on average, achieve lower results.
Schools like this would not satisfy the fans of the super-selectives; their effective catchment areas would be, perhaps, 20,000-40,000 people if you had fixed, unique catchments, somewhat more if you allowed parental choice of schools. At any rate, far fewer than the millions who live in (sort of) commuting distance of Queen Elizabeth's School, or Henrietta Barnett.
And proponents of mixed-ability teaching would object to setting.