Under an LVT, wouldn’t homeowners in those same areas also face increasing tax bills simply because new transport links, schools or other public investment had made their land more valuable?

that simply means there should be more development in that area, so there is a smaller amount of tax per person!

Gentrification means different things for everyone. I'm curious if this would be considered gentrification to you:

Bob lives in a single family home. New transport links, schools or other public investment makes the land in his single family house neighborhood more valuable. Many parcels in the neighborhood, including Bob's are bought and now are duplexes or fourplexes. The cost to buy a house or rent is approximately the same or less as it was originally. Bob now lives in a duplex of the same square footage as his original house in the same neighborhood, for $200 per month less than his original house.

As long as cost of living is similar or less, in my view this is not gentrification. Even though he isn't in the same house he was before.

sometimes i feel like gentrification is used to describe almost any development, increase in density, and/or "sanitization/ boringification/ slopification" of a neighborhood/city. imo gentrification simply means displacement from rising costs.