The increase in land value over 30 or 40 years has gifted them with lots of home equity (far more than their principle payments on their mortgage). That's enough funds to downsize from 3 or 4 bedrooms on a 10,000 or 20,000 sf lot to a very fine single-level apartment or condo in a building close to the center of things, a home they can take care of, feel safe in, and perhaps even have services to cater to their current needs, just as the nearness to schools and jobs catered to their needs 30 or 40 years ago.
Meanwhile, young families, particularly those with only one earner, must drive further and further to qualify for a mortgage. They drive not just on their home-hunting trip, but twice a day to commute to jobs close to those family-size homes and well established schools.
And if they do manage to afford a home in those older more central locations, they are paying (in California) multiples of what their neighbors are paying in property tax. Those neighbors raised their kids in a time when people of all ages were contributing to the costs of the schools. Today, the young families pay lots, while the comfortable older ones play little.
And from an environmental POV, having those workers commuting 30 or 40 miles each way each days isn't such a great deal for the environment, or for their quality of life, or for the time they can spend with their children.
About (2): LVT has no incentives or disincentives for how you use your land. It's entirely up to you, your tax is the same no matter what you do with the land. That's why an LVT is economically efficient: it doesn't mess with market allocation or land use.
Why would green space be reduced? If green space is the best use of a given plot of land right now, an LVT doesn't change any of the incentives nor opportunity costs at all. (Also keep in mind that many green spaces are zoned exclusively as such. LVT doesn't influence zoning.)
LVT concentrates development efficiently. It would actually increase green space, since people wouldn’t have to develop sprawling exurbs to escape high rents (too little housing) in the city center. So no, LVT would produce significant quality of life improvements over what we have now.
Not in valuable parts of cities it wouldn't. The direct effect of LVT is higher cost of land and lower cost of buildings, thus incentivising more building and less bare land/green space.