In the US we have tax-exempt businesses, but I don't think we have partial tax?
Yet it seems like a host of businesses provide value to the community that would make up for their property tax income. Full service grocery stores, child care, etc.
Of course, in reality businesses would expand their margins as much as possible. But at least they'd be there.
We can both probably agree that real estate property value has a loose correlation with actual value, and is subject to a large number of external factors. Not least the suboptimal-for-community inflationary pressured California is infamous for.
By partially abating taxes, you're simply adjusting profit calculation for a plot of land for a specific use.
Now that I think about it we already do this, just in more coarse grained terms, via zoning. C3 is taxed one way, R3 another.