Indeed! A few points just so people who haven’t heard of LVT before don’t walk with easily addressed misconceptions:
1. The government today assesses land value. It also must assess the value of far, far more nebulous things that can be hidden, transfigured, created/destroyed, or moved offshore. Yes more importance would be tied to this singular assessment, but this assessment is singularly easy to assess!
2. The price/value itself would be set by the market. The assessment of that value, of course, would be by the government and you are correct there is risk of differential here (though mitigated by point 1)
3. Lastly, because land cannot be created, destroyed, or moved, a tax upon it is uniquely unable to either incur inefficiencies (deadweight loss) or to be passed onto tenants/consumers. This is contrast to every other form of taxation, which incur inefficiencies then get passed onto the consumer in the form of price increases anyway.
My only issue is that you end up making the govt more of an arbiter of what "value" is than it already is, which can end up causing issues.