Yes, of course. It's impossible for "equality of opportunity" to exist as long as private schools exist.
No child deserves a better education just because their parents make more money or have better connections.
And yet that would happen even without private schools, just based on geography.
This is a good point of course, but would be rectified by other measures. I wouldn't implement busing practices, but I would like to see more affluent communities better integrated by including working class housing. Abolishing private schools would only be one part of a plan of implementing "equality of opportunity" for all.
I can understand the resistance in the US to such an idea, especially on a forum full of Whites who went to private schools. The public education system in the US is so deplorable, that the idea of forcing everyone to go to a public school sounds horrible. Such a move would require a huge overhaul in the public education system first, of course.
Keep in mind I am coming at this from a Canadian perspective. Very few Canadians send their children to private schools. Even the Prime Minister, a conservative, sends his children to a public school (though, it is located in the richest area of town, as that's where his official residence is).