"Keeping them alive is inefficient for the species."
A lot of that is based on the idea of a nuclear American 1950s family, mom dad and 2.5 kids in a house and grannie lives in Florida 1000 miles away.
More likely, if I lived for 1000 years I'd spend a lot of time ensuring the economic success of my descendants by teaching programming, electronics, maybe math unless a better mathematician comes along. If this situation existed in the past, I have a GGGGG-uncle (cousin?) who was a Harvard literature prof in the early 1800s and I'm sure he would have taken a decade out of his semi-eternal life to educate me on English lit and related topics. I have some GGGG-Uncles who were in the civil war and fought in Tennessee, surely their personal experiences would have more impact than merely reading a book.
This has certain economic and evolutionary effects, such that a "migrant farm harvesting laborer" not allowed to ever benefit from his own labor, would not be able to help his GGGG-grandkids in any obvious way. So some kids are going to grow up with 16 hours a day of continuous one on one academic tutoring from a team of perhaps a dozen PHD ancestors, while other kids are going to grow up basically playing video games, or at best, watching youtube videos.
Its an obvious sci-fi topic to explore the nature vs nurture question. A permanent overclass would likely develop based solely on ancestry (indirectly "nature" although in practice "nurture")
This is aside from obvious social interaction. Locally I know a lot of the people in my field, and a descendent going into my line of work could be financially (aka reproductively) rewarded by hanging out with me and meeting people. If I do nothing for a descendent other than socially introduce them to local hiring managers, that's still genetically a net win. Everyone else will be doing the same thing so I will have to keep up.