The value might be affected by the tax, I suppose, but the person buying it would be affected by that too when they came to sell.
Land value tax is based on the premise that if you are land-rich, you should also be "more productive" to earn the right to keep the land.
Final point; apartment buildings generally have a lower land value than you might expect given the sale price (see my other comment), with a small square footage spread over many apartments in high-rise, the tax may well be less than you expect (i.e. much of the value may be in the rebuild cost.)
During communist times local factory provided flats for the workers. After factories were closed, government formed cooperatives to manage real estate. Currently, buildings are in complicated legal state. There was one period when current tenant could purchase the property for 10% of market value, but it was blocked (possibly by developers lobby). On top of that, some buildings and land have unknown owners because of WW2.
I'd love see an experiment when income tax is replaced by land and property tax.
Avoiding any adjustment in ownership patterns seems impossible to achieve without strong legislation, but attempting to provide adequate compensation through the market (rather than the government) seems like it might work? (question mark because I really have no idea...)
Far more effective for them, would be to sell the valuable property and buy something they CAN afford the taxes on. Better than bleeding them dry by a large margin.
You're right that selling the big house and buying a small house makes sense for a lot of seniors, but taking away their ability to choose something like a reverse mortgage is just patronizing them.
But I imagine nobody in their right mind would deliberately go broke when other options were available. I imagine that folks that work hard to convince them to do such things, are not working in their favor.
Patronizing them would be, deciding that a reverse mortgage is always in their best interest.
That way, people get to live out their lives in their properties and the state still collects their money.
I would call it, an undeserved prize for the working class. Undeserved, because they had nothing (directly) to do with the rise in prices.
In 1970s and 1980s there were a lot of apartments built by communist government, most of which were given to average citizens either for free, or for some insignificant amount of money. Now almost 40 years passed and we ended up with millions of people still living in those apartments, which they got back then, or inherited.
Now, especially after Poland joined EU, market price of those apartments skyrocketed, while owners income levels stayed pretty low. So, if government introduced land-value tax most of those people would not be able to afford paying it, effectively forcing them to sell their apartments.
I don't know how such tax would work in different setting, but here in Poland only visible effect would be rich people taking over properties for discount prices.