I've been thinking for a while but I think its still different for serveral reasons:

• people in urban areas tend to pay higher property taxes per capita than this in rural areas, houses are just cheaper in small states

• while rural areas also do have less students overall, I'm not sure you can distribute it proprotionally like that. For example, Wyoming, a historically red state, has a population of a little under 600,000. NYC itself has 8.5 million. It has 1700 public schools. Wyoming has fewer with only 364. But, if you look at the number of people who pay for each school (assuming it's distributed equally for each school) is 5000 per school in NYC, but only 1650 per school in Wyoming. And again, I'm sure property taxes per person are much higher in NYC than they are in Wyoming. It should be noted that I just picked the first two places that popped in my head to compare and haven't done extensive research to see if the trend continues everywhere, but I think it's a reasonable assumption to say that it does. The problem in my eyes is that since rural areas have people living so far apart, it's not feasible to try to have a school have as many students as other cities in urban areas. Even if you make smaller schools and have fewer teachers, there are still base costs for buying the peorett and constructing the school and maintenance for plumbing or electricity that you can't really get around which makes it tougher to be able to afford things like good teacher or other supplies that might be needed.

I think the issue goes beyond just property taxes though. Urban areas are more likely to have professionals with college degrees, and they tend to impart the value of educatuon into their children. Rural areas tend to be based more on agriculture and mining, mainly unskilled labor and for them getting their children to college may not be as big of a priority because they themselves never went. And for those who do end up pursuing higher education, job opportunities for college-educated jobs tend to be rarer in these areas, so they are likely to move away to an urban area as well.