Plus, evolution will be your downfall. Specifically, you'll get to see humanity evolve into something… else, while you're left behind like an Austrelopithicus in the modern day.
Also, ageless immortality doesn't say anything about invulnerability. Get trapped in a rockfall, every bone in your body broken, agony beyond measure, and know that you can't die. And even IF we add invulnerability, you're still trapped in that rockfall. So instead of unending pain, now you get unending boredom and sensory deprivation. If/when you're eventually freed, you're insane.