FOMO, quite literally.

Quite hard to enjoy the current times if you're dead. I would take my chances with the immortality even in spite of some vague "dark ages" hand-wave scenario, thanks.

Well, if there is a immortality drug, it won't be cheap. So only the rich can get it, who will then live longer, and have more time to accumulate wealth, while thinking, "the earth is already overpopulated. If the drug becomes too cheap, that problem will worsen" So it will stay out of reach for the masses.

So the result will likely be immortal overlords and mortal peasants. Hard to see any other outcome.

As long as we're writing science fiction, if immortality was known to exist like that, there are swathes of ordinary people who would stop at nothing to obtain it. Perhaps the cure IS cheap (how could you know for certain it's not?) and it's not an issue in the first place. Perhaps some of the rich will not be so cynical and give immortality to the finest minds in the world, allowing scientists to build knowledge indefinitely instead of whole generations of knowledge and experience being permanently lost consistently every 80-100 years. Perhaps those scientists with massive amounts of experience thanks to the time they now have bring about a utopia.