Mine does that too, but the process is clearly flawed because you can't buy land for the assessed price, and you can't build a structure on that land for the assessed value.

Just because it’s not possible to separately buy the structure or the land doesn’t mean the numbers are wrong. The point still stands that taxing land disincentivizes nothing while taxing structures discourages building them. Many towns in Pennsylvania had a pretty good track record with this. They implemented a mixed tax system that focused more taxes on land and less on structures because they wanted to make people sitting on empty land and not using it pay more. They also didn’t want to penalize people for upgrading their home. The system was extremely successful in its aims.

Rebuild cost and current value are different, given that new construction is worth a premium

It works because they just need to come up with a total value and how it divides between land and house doesn’t matter much. My property taxes also separate out land and it puts the land at like 25% of the total value, but in reality someone would easily pay >50% for my land just to demolish the house and rebuild.