LVT isn't a market distortion. Private landowners getting rich by not doing anything is a market distortion. If you buy a building (say that isn't rent controlled) and over 10 years the market rate for rents in the area doubles, you didn't make that happen basically at all but get to reap the rewards. That doesn't make any sense -- the community should get that money as the community created it!
On the other hand if you renovate a building and now can charge twice as much for rent, that hardly effects the land value at all -- it's one building in the area, it won't have a huge effect generally on the land value of adjacent buildings. So you'd get to reap the rewards of your work -- you improved the property and now get to make money from that improvement. LVT explicitly does not tax improvements, only the site-value of the land.
I'm certainly for eliminating rent control and massively liberalizing land use (you may still need very broad classes of zoning, ala Japan with 12 total zones all of which allow mixed use and multi-family dwellings and non of which except industrial zones restricts the minimum size/use in an area, but my preference would be to just have a separation between industrial and non-industrial use cases). That would help a lot! But it doesn't address the fact that when for instance Los Angeles installed the Expo Line for ~$3.5B the people who owned apartments nearby suddenly got a massive 20+% boost in the rent they could charge, a total value of which would have been large enough to pay for the line's construction & operation!
The value of that public investment ought to have come back to the city to be spent on yet more improvements, not pocketed by private property owners who happened to buy a building nearby a decade or more earlier.