The idea of biological immortality terrifies me. Like other commenters have said, the risk of power being further entrenched in the rich is basically an inevitability. Biological immortality under capitalism is pretty much a guarantee of immortal god-oligarchs that will control a bigger portion of resources and power than they do now.
Also it removes death as an unbeatable end. What if there were still robber barons from the early 1900s alive today? We'd be worse off politically than we already are. Death is an integral part in the march of progress.
From a personal standpoint, I'm not super jazzed about living past my 80s even if I didn't age and was in perfect health. If biological immortality comes to be I'll still punch out around 90 at the latest and update my will to prevent my consciousness from being uploaded to San Junipero.
The sweet abyss of oblivion worked for me from the beginning of the universe until my birthday, it'll work fine again when I get back to it.