Yes, by design. One major goal is to prevent a landowner from squatting on an empty lot while their neighbors build prosperity around it. The "squatter" then cashes in, having done nothing themselves. "Everyone works but the empty lot" is the commonly used phrase.

The goal of an LVT is to insulate a landowner's tax bill from being affected by their own improvements. Its anti-goal is to insulate a landowner from changes in land use around them.

Another benefit is that it encourages more efficient use of land. Existing taxes mean that if you demolish a high density retail strip and replace it with a McDonald’s or Walmart with large parking lot/drive thru, the tax income plummets while the cost to maintain the roads and plumbing remains the same.

Just to be clear: land value taxes by themselves don't encourage more efficient use of land. Removing taxes on improvements (and on capital and labour) encourages more efficient use of land, and a land value tax can help finance those other tax reductions.

It’s just strange phrasing that improvements increase the value of adjacent land but not the land they’re on.

It increases the value of both equally

Think of it as part of a communist plan and you'll see the why and who start to make sense.

True enough. It doesn't factor in land improvements directly into the calculations, but it could be affected indirectly by whatever the market seems something to be improving the neighborhood in general.