I think the problem stems mainly from the factor most people don't figure into discussions about taxes and schools. In most places, schools are funded from property taxes. While Joe Shmoe and all his neighbors diligently pay into those funds, government has been giving "incenctives" to businesses to move into their towns and communities. (i.e. reduced taxes, including property taxes) This means that some of the largest holders of property by value pay little tax. This reduces funding for the schools.
In our area, there's another factor. For decades, all the schools were operated at the parish (county) level, however, local communities were taxed in part based on their own district for their own school within the larger parish. In the early 2000's, one such district voted a bond issue to improve their schools. The larger parish this district belonged to has an urban center that is a sucking black hole of financial need. The district that voted the bond issue is a small town with more than its fair share of middle class folks.
Well, the parish school board decided to use the money that this district had voted to pay in the form of taxes for the urban school instead of the district. The district sued to put their schools under their town charter (but to include the large unincorporated community as well).
It came to a statewide vote and the community got their own school district. Since then two other communities have forcibly left the parish schools for similar reasons.
Now, that said, the parish involved has a huge petrochemical plant and plenty of heavy industry. The major city is not poor, but for decades most people have sent their kids to private schools because the schools in the city are horrible. I think that too many incentives have, over the years, been given to too many people while, property owners of homes have been loath to fund the public schools as they don't have a horse in the race, so to speak.
The solution?

So far no one has tackled the core problem because voters don't want it tackled, so the solutions that are tried will inevitably fail, as they're all just noise that don't touch the real problem at hand, which is apathy about the tax base.
I live in the city that sued to be independent. So far, no taxes for schools have been voted down and the city has been very cautious in how the tax base is handled. We've had the top rated school district in the state for something like 5 years now. And the kids, while they have very intense school supply lists, go to school in well-equipped classrooms in nice buildings. There are programs for every type of learner, from the kid who is on track to get a full ride from a top tier school, to the kid who is in danger of dropping out, and everyone in between.