So, because land value assessments are easier than property assessments, we should get a smaller margin of error by switching to a LVT. This is good.

Your other point seems to be that no margin of error is acceptable and we should therefore ditch the whole thing.

It's not clear that the societal pain from somewhat inaccurate tax assessments is great enough that we should just set everything to 0. We have lots of data that 0 property tax leads to housing shortages and rampant speculation (cf. Malta for an example) and if you don't tax land ownership you often end up taxing something productive, like income.