What about the old people who didn't buy a house a long time back and now face high rents? Why is it always a selective group of old people we are supposed to carefully design policy to perfectly accommodate?
High enough land value tax, consistently applied, will make the land cheaper and affordable to said old couple, because it neutralizes the phenomenon that land continuously increases in value as long as the population keeps growing.
Because home equity is highly liquid. You can refinance your mortgage (and take money out), or take out a reverse mortgage (which pays you monthly in exchange for eventual ownership), or a home equity loan. Tons of ways to turn your home equity into cash.