These problems do appear inextricably linked. Individualism in american culture is, IMO, the root. In many other cultures, family is huge -- folks are connected to their parents, grandparents, siblings, cousins... grandparents help out with the kids until they can't, and the skills of parenting are naturally passed from generation to generation. Funny to see a comment on another that "no one" is prepared to raise a kid... that's because individualism is bad at retaining wisdom.
The problem with your mixed old folks' home / orphanage is that individualistic old people don't wanna live there until they're too old to help out.