Then the government should advertise an explicit minimum amount of tax paid annually in order to register for the school, or switch property tax to land value tax only.

The residency requirement is that minimum. It's not a minimum in monetary limits. It's a minimum that you have to actually live there. The fact you are living there means you are paying a higher tax amount than for an undeveloped lot. There's a difference on having a house on a lot vs just some field. You have some skin in the game as they say compared to just owning land while living somewhere else completely.