You have that system now, especially in public schools. Take a look at the property taxes in the areas with nationally recognized public school systems (see Great Neck, NY, as an example) and home prices in those same areas. Add into that its almost impossible to find a legal rental apartment in the area and what do you have.
The voucher system is the way to level the playing field a bit. You can't compare elite private schools, they will always be about who can afford to attend versus who should attend based on aptitude (with some notable exceptions, such as Regis). Anyway, they are private schools for a reason.
I was more talking about more efficient and better public schools.