This is natural, but also, myopic.
The dividends of research into immortality are incremental, but each breakthrough has the same outcome: increased quality of life. Humans become healthier; eventually, we last longer.
Yes, at the limit, there are problems with immortality: Sterling's Holy Fire is a great exploration of the problems a gerontocracy could pose, as is Morgan's Altered Carbon. Without older generations dying off, would there be any room for the young?
I submit that these would be excellent problems to have, that there is no guarantee we will ever have them, and that the dividends from trying to earn ourselves such problems would be considerable.