The greater good is that you don't force people out of their homes. If you worked at 1960s-1990s pay, there's no way you're affording $30k a year in tax, so it makes sense to lock it at the purchased value. Sure the child inheritance of the old tax rate might not be. The real question is why not use income tax? This would avoid kicking out the elderly, and only collect money from those who are actually making it.

I don't generally like the idea of taxing people on things they already have. I would rather see it on the people who are making money. If you are benefiting from the system (income) then pay part of it (tax). Under these other schemes, it could be that the system has failed you, left you behind, etc and then the tax is like the nail in the coffin. It makes the most sense to take the money from the people who are making it.