LVTs can't fix sky high real estate prices as that's principally a problem with zoning. In fact, communities can and will and do (remember, as the article mentions an LVT is hidden inside traditional property taxes) use zoning to prevent assessment increases.
Fixing zoning will do much more to address inequity than even a complete switch to an LVT. Don't fix zoning and LVT won't actually accomplish much of anything. That's why you see similar patterns of development across the board, regardless of LVT. When homeowners begin to feel the displacement effects of LVT, one of two things invariably happens: LVT is dropped (or otherwise moderated--e.g. geographically selective decreases in tax rate), or development is restricted through zoning and similar regulations.
LVT is undeniably a great solution, it's just a solution to the wrong problem.