And if you read the linked paper, particularly the section "Effects of Reassessments on Split-Rate Taxing Bodies" (split rate being the riff you're referring to), making land value assessments more accurate of course makes land value taxation more appealing.
Property taxes have a component that redistributes wealth from landlords to the working people, but it also has a component that penalizes making better use of the land. The former is usually called "land value tax" and the latter is the part of the tax that is proportional to the improved value of the land. The latter part incentivizes some uncertain amount more towards mcmansions and away from multi-unit buildings.
Property tax also encourages speculators to hold and trade underutilized parcels compared to land value tax. With property tax, the penalty for holding an empty parking lot in a dense urban center is much lower than under a land value tax system.
That’s one approach, but then you get people playing with the system, adding a single apartment to the multimillion dollar lot, or the aforementioned parking lot (technically a business). The great thing about LVT is that it bypasses these shell games. The biggest weakness is that you have to fight off any attempt to seize control of the valuation process, and that is going to be difficult except in places with highly engaged and intelligent voters.
And if you read the linked paper, particularly the section "Effects of Reassessments on Split-Rate Taxing Bodies" (split rate being the riff you're referring to), making land value assessments more accurate of course makes land value taxation more appealing.