My mom is a Geriatric and Alzheimers specialist, so I kind of know what you're saying here. There are some elderly people with disorders such as dementia who are better off in a nursing home, and usually don't even realize they are there, but there are certainly others who could live at home, if not by themselves.
You have to take into consideration though, that often it is a lot of work to care for an elderly person who cannot care for themselves. For some families to have the time to take in an elderly family member, it would mean rearranging their entire lives, and sometimes thats not reasonable. Just because they can't make the time, doesn't mean they don't care, necessarily. It costs money to keep someone in a nursing home, so either way the family is feeling it.
The saddest thing I've ever seen though, are elderly people in nursing homes who never get visited by their families. I think that thats the big issue here. Its not so much that they're in the nursing home, but that they feel completely cut off from their families, because no one cares enough to drop in and say hello. My eyes are welling even as I type this. I've helped my mom out in some of her homes, and I've had people beg me to call their sons or daughters for them so they'll come in to visit. I am absolutely appalled at how people can just conveniently forget their relatives like that.