Parents making sacrifices regarding their child's education is the greatest indicator of success. That commitment might be monetary or time.
How do you know that a school is a crap school or not?
The test scores that everyone despises.
The public schools do not want to lose the student population(less teachers, less administrators needed) that the empire is built, but also do not want to lose their better scoring students that raise the schools scores.
As far as tax credits/deductions are concerned, my wife's hometown church runs a parochial grade school. The school is tuition free for members of the congregation. You are strongly encouraged to put your tuition in the offering plate to be able to have the tax deduction, but like any religious donation, it's up to the individual.
As with all human endeavors, some people will take advantage of a situation.
I'm going to say some severely controversial things here, so I hope you won't misinterpret my intentions. I have spent a number of years (10+) working with public school populations in california with a NSF funded program and have spent the last 3+ years as faculty at a private university. You are right with you assessment above. Many people take advantage. Here is my take:
1) By and large, teachers are very competent individuals who are underpaid for the service they perform. The lack of compensation and an idiotic, antiquated application of teachers unions, pensions, and tenure generates an incentive structure where the majority teachers only do the bare minimum to stay employed.
2) A disturbing fraction of students, and by extension their parents, do not take school seriously. We live in an era of unprecedented resources and access to information. Going to school is a privilege that should be taken seriously. Of the students that don't take school seriously, the generalization is that they largely come from *either* wealthy backgrounds or poor backgrounds. Parents of these students treat school as baby sitting. Folks from the wealthy backgrounds send their kids to private schools and ancillary education (Kumon, SAT classes, etc. ) at a disproportionately higher rate. This access of *even more resources* does not translate to better performance at the rate it should. Folks in the middle are fairly opportunistic with public school resources.
3) A majority to students do not need to go to higher education for the vocations they choose. Many students don't even go to school for the education, but instead for the experience. If you can afford it, great, enjoy the ride. If you can't, and depend on scholarships, you should be held to a minimum standard of effort. The higher education industry including the University of California system and the University of Kentucky is not a sustainable enterprise. This is a bubble that will burst. When it does, people will take public education more seriously.
To sum it up, education is an opportunity that comes at significant time and money costs (for the public), not an experience. If we need to transform the system so that people take it seriously, we should consider having families pay for public schools and pay teachers significantly better salaries.