If you fund your schools with tax on property, the amount of money you need scales with the number of residents you have. So now you have to distribute those liabilities across land value rather than per occupied units, that could lead to some huge distortions (a 100 story apartment with 200 kids paying negligible taxes while a single family home paying for 200 kids while they only house 2).
Local councils do collect a "council tax", but it's basically a fig leaf to disguise a poll tax by just enough that people don't outright riot: https://en.wikipedia.org/wiki/Poll_tax_riots
And in practice, council tax is only about 55% of local council's funding, the rest coming from central government. And the councils do sometimes go (effectively, but not literally) bankrupt: https://www.bbc.com/news/uk-politics-66878229
How wealthy would a family have to be in order to live in a single-family house on a piece of land so valuable, so centrally located, that its value could equal that of the land hosting a massive high-rise? This sounds like a very progressive form of taxation.
There is a lot of housing that is unimproved because the owners can't afford to improve it. E.g. you bought a long time ago, or it is used as low income housing now (conversely, in my neighborhood at least, the low income housing is older and less dense than the shiny new dense luxury apartments). The only recourse for that land is to convert it into a tower of new luxury apartments, gentrifying and pushing out whatever poor folks are housed in it now.
There are other ways to game this, there are always arbitrage opportunities when a tax isn't aligned with its expenses.
