Your question is easily resolved by looking up how much American schools are funded, compared to historical funding, other countries' funding, and their relative successes.

Outcomes aren't any better with lower ratios. The best-funded public schools have funding higher than anywhere else, in the world, and have poor outcomes... it's not a funding problem. And it's difficult to "value teachers" when we learn of these outcomes, it runs counter to human nature.

Private schools are (excepting the truly 0.01% which are the most elite schools meant for the children of billionaires and statesmen) are nothing more than public schools dressed up in $20,000/yr tuition so that the upper middle class can feel special. They draw personnel from the same pool of teachers, they use the same textbooks and pedagogy. They are essentially public schools with a new label. But that you think I might be talking about private schools shows how you can't even really think about alternatives. You don't have the mental language to do so.