That is certainly a problem, but as I say that $1m will be earning some interest until the end. And you have to be doing very well to be fully active after 85, or 90 at the latest, so commuting your house into a retirement village or apartment for the last few years on the state pension wouldn't be the end of the world.
My uncle lived on the state pension until he was 97. Quite contented, especially after his wife died