The "failing" urban or rural public schools are under the fiscal control of the school boards, and these usually are composed of business persons, not educators. And they usually apportion the funds in selfish ways, not ways that would necessarily best serve the education process.
As an example, the two years I taught in public school, I was the one "co-op" teacher in two small neighboring districts - I taught 3 morning classes at one school, and 3 afternoon classes at the other school. With both districts combined, there were 22 K-6 teachers; 2 art, 3 agriculture, 4 business, 5 English, 5 history, 2 English as second language, 2 home economics, 4 special education, 4 science, 5 math, 1 math & science, 1 ISS (in school suspension) (?!?), 8 coaches (plus 3 assistants/aides) and 1 music. Some of the buildings were not in the best of shape, but each district had a well-built, well-maintained athletic field and gymnasium. At one school, my classroom (and I was the only one who used it, it was not "safe" for any other classes) was the old gym - holes in the floor, broken windows, and a hasp & padlock on the door. One of the schools, though, had money to have thriving well-equipped programs for football (new home & away uniforms every year), cheerleading, boys' basketball (ditto with the uniforms), girls' basketball (uniforms again), baseball, softball, and golf.
The concept of pulling bright but poor students out of the public schools and giving them vouchers for private schools is not a good one. Perhaps a better idea would be to restructure the allocation of funds within a school district, track down and eliminate waste within that district, and fix the problem at its root.
Not to mention that using public tax money to fund tuition for select students at a private school just is not the right thing to do.
Oh, and JustAsking, thank you for making the distinction between conservative, liberal, and progressive.