Re: Too much tax.
Well, this isn't wholly and exactly true:
"The principal problem with building new stuff is that it reduces the price of nearby existing stock"
Land in Mayfair that you can build a house upon is worth a lot more than land in the middle of Sedgemoor that you can build a house upon. Largely because the former has 10 million other people living around it and the latter has, well, no one.
And the point of an LVT is to tax that increase in value that all those other people (plus the sewers, the roads, the Tube etc that have been built) add to that piece of land.
That said, sure, if you extend the city one more row of houses out into the green belt then you reduce the value of those houses that used to be the last row before the green belt.
It's not entirely one way or the other.