LVT doesn't punish or reward any land use. That's the whole point of the argument behind it not having any deadweight losses. LVT is the same, no matter how you use the land.
The opportunity costs between different land uses is exactly the same with LVT as without.
To illustrate more:
Without LVT, when you use a plot of land costing x dollars that you own outright, you 'pay' the opportunity costs of not being able to employ those x dollars elsewhere (or rent the land out etc).
With LVT, the price of that plot of land will adjust to y << x, so that the total of LVT on a plot of land costing y and the opportunity cost of y, will equal the opportunity cost of x amount of capital.
(This discussion ignores risk and other taxes for simplicity.)
Slightly off-topic: I'm also against capital gains taxes. We want more capital employed, so that workers become more productive, and so that the different providers of capital compete. So if anything we should encourage more deployment of capital, and capital formation rather than consumption of wealth.
(Also thanks to international mobility of capital, I suspect that a big part of the burden of capital gains taxes mostly falls on the users of capital, less on the providers. But I am not sure there.)