Property taxes (specifically on the unimproved value of the land) offers a way out of this dilemma. If you can do more valuable economic activity with a piece of land, you can and should pay more for it, so it'll be worth more. So if you spend $10MM/yr in financing for building a bridge, and it increases land value in the catchment area by $100MM, and you have a 12% land-value tax, the state responsible makes more money.
The old person will make a good amount of money selling their home, and they can use that windfall to buy a nice new home somewhere warm and cheap, so it isn't like they're being trampled on.
It deconstructs communities.
This land is too valuable to allow you people to squat on it. We'll compensate you, so it's all fine and fair, now get out.
It's not hard to understand why people don't like being treated that way.
Subsidize? I think your concept of private property rights is under developed.
This is the gigantic pitfall of overly-individualistic property rights - that socially beneficial infrastructure development doesn't happen, because nobody has the power to siphon off enough of the value created to make it worth doing.
That is so wrongheaded I don't know where to start. Increasing property taxes is the exact reason you have older folks be forced out of their homes after having lived there most of their life.
No one should have a continuously growing tax burden over time.