It's hard enough being a nerdy kid today. Such kids almost always are in decent places because kids tend to be like their parents. Kids with the potential to succeed come from parents with the potential to succeed.
Education doesn't work if the classroom is full of kids who can't behave. Education doesn't get very advanced if the classroom is full of kids who aren't bright and willing to study.
Mix things up, and what do you get? A few strangely poor-yet-viable kids will move from very bad schools to slightly bad schools (nice but insignificant) while all the bright promising kids will end up in less-effective schools. The best schools will cease to exist. (by changing that is; they don't physically go away)
It does make us more equal, largely by inhibiting the success of our brightest and hardest-working students. Is this what you want?