IMHO, the single biggest proof that money won’t fix the problem is LAUSD. When you look at the actual total expenditures across all funds and categories (i.e. icluding building new schools), over the last two decades, they’ve been spending close to $20,000 per pupil each year.
LAUSD is, IMHO, broken. Horribly broken in spite of many dedicated and competent individual teachers. They are sadded in a system that strips them of resources, saddles them in bereaucracy, structurally creates a hostile employee/employer relationship and tolerates mediocrity and covers-up failure in denial and cares more about politically correct talking points than accomplishing anything concrete.
And anecdotally, the schools will have no problem hiring at current compensation levels. Much like LAFD, they get too many candidates. There is zero need to increase teacher compensation, the recent grads are literally beating down door, smoozing everybody in every school they can find trying to get one of few openings.
If you can’t find math instructors, you raise compensation for math qualified instructors, not raise compensation for all instructors.