Except you get exactly the same opposition in places where schools are funded by a higher level of government

and if anything you taxes will go down because they are now spread across more households.

I can't answer for different states and municipalities, but I know about mine and NJ based on how we had to expand every school in the district over the last 10 years.

These are big capital expenses. My property taxes have never gone down, even as my township has expanded.

Part of this is that taxes are calculated on assessed value. Where I'm at, assessed value is a combination of lot size + structural improvement. Tax bill is assessed value * rate. Assessments have never gone down. The more people want to move here, the more values go up, the more capital projects need to be undertaken before new tax payers are contributing. It may take years to build a new development, but the multi-million dollar budget to expand the school and staff up teachers has to happen in tandem, before the new tax base exists.

My lot is from the 70's. It's huge. New lots are significantly smaller. Townhouses and apartments are very dense. New development does not yield savings in taxes in practice unless it is commercial development.

A big piece of farmland contributes taxes, but requires little in services. Convert that 50 acres into 50 units and now you need much more services and infrastructure compared to the 50 acre farm.

You underestimate just how much schools and teachers cost. Those 50 units might add 50-100 students. Capital projects start even before the units finish to prevent overcrowded schools. Contracts are signed for garbage and snow removal if 5 of those units are occupied or 50.