I read this as sarcasm, but I re-read it and am not so sure?
I hope you're will to pay for that in blood because there will be war over it.
We get that there's no such thing as a perfectly level playing field, but we're not going to allow children to be raised by the state to achieve what will be frankly in all likelihood not much of a gain in that regard, and a loss of basic freedom, and that's before the obvious risk of totalitarianism.
If you're worried about the state reading your emails, or net neutrality, you should naturally be 100x more concerned about what the state wants your child to believe.
While I am actually in support of good basic public education, I suggest the issue is important enough so that it should be at 'arms length' from the politicians, much like the Central Bank, but with more public input.
We need to get rid of this notion that there's really such a thing as 'perfectly equal' anyhow. Comparative Value. People value different things. Instead, take the approach of 'if there's a will there's a way' i.e. every kid gets access to good, basic, core schooling, and if a kid is motivated and has basic talents, they should have access to basic higher education.
Finally, most of the needle has nothing to do with quality of education, which most kids have access to, it's the quality of their home life. I'll bet material improvements in minimum wage and some kind of basic 'healthcare for all' would yield materially better results for kids than any specific changes to schooling, other than the cost of higher ed.
Edit: thee are enough examples of great public schools i.e. Norway, S. Korea, Canada, we don't need to get all theoretical about it. Work on 'all the issues' and the kids will be mostly ok.