It would seem to be a mistake to generalize across the entire nation, and basing your analysis on a denominator of school districts will be weirdly biased; better would be on a student-weighted basis.
Locally, i can tell you that despite the bulk of funding coming via the state California district spending per pupil varies widely. The quite adjacent districts of Fremont, Oakland, and Piedmont spend $10k, $14k, and $20k per student, respectively.
The funding levels are per capita obviously. And the point is not that funding levels don’t vary, but there is no systematic bias toward richer districts. Around here, for example, Baltimore and DC spend far more per student than the rich suburbs surrounding them.
You analysis was stated as "most states show ..." when the fact is you can add up the population of "most states" and not get anywhere near most of the people. So it's a mistake to think that way.
Locally, i can tell you that despite the bulk of funding coming via the state California district spending per pupil varies widely. The quite adjacent districts of Fremont, Oakland, and Piedmont spend $10k, $14k, and $20k per student, respectively.