And so what?
These people are still human beings. They still deserve life: If dogs deserve no-kill shelters[1] then humans also deserve a life. They deserve a chance to live out their days, and to tell stories to their (perhaps prolific) kids and grandkids (who also deserve a healthy life, and that includes having a healthy -- if piss-poor and inept -- family that includes their elders).
Right now, it often works like this: They live in squalor, and have broadly have nothing of merit. Their kids -- if they manage to thrive -- disown them. And the whole time this very real person is still alive (if they make it that far), their grandkids only know of them through photos.
That's no life. Not for the senior, the kid, or the grandkid.
We can do better than that. It will not be cheap, but we can afford it, and we'll have a healthier society as a result. People, and the families they create, are important to the healthy existence of everyone in a society.
[1]: We can certainly talk about assisted suicide for humans or just culling the herd as options that may be superior to leaving folks to die in the gutter, but isn't it easier to just avoid that topic and give all humans a stable and reliable chance to stay alive? How much does that cost, do you suppose?