LVT sounds good in theory, but a large number of rich people _are_ acting as rent seekers (they own property, and extract value via rents on people who work/produce actual value on it). It would not be politically feasible, unless the gov't is prepared to fight against those powerful land owners.
Yes, the political feasibility is one big problem. (The other challenge is to figure out how much revenue you could raise---there are some good theoretical arguments that elimination a tax on something else like labour income should increase the local land value and thus land value tax by enough to offset that loss, but I don't know whether that works out in practice.)
There is some hope for the political feasibility: some countries already have land value taxes with various imperfections like Estonia, and some Australian states, and some counties in the US.
