The study [1] doesn't look at state-level averages, but uses school-district-level funding and demographics data.
> there are public schools in Boston and NYC that have endowments larger than the total budgets of a dozen other schools combined
Table 1 from the study also includes funding standard deviation data (the "SD" column). The highest one is $765, meaning that 99% of schools are within 3x that amount around the mean. There may be outliers like you say, but they are statistically irrelevant.
https://journals.sagepub.com/doi/full/10.1177/23328584198724...
A common myth - federal and state governments supplement school funding to roughly equalize per-pupil expenditure. See my other comment: https://news.ycombinator.com/item?id=47357203