'Immortality' would not exactly be very great. Realistically speaking you would still be able to die, it's just that your cells would not cause aging (and even then with this cure the cells would still have issues) and this is known as negligible senescence (and this is actually found in lobsters and some jellyfish). You would still die from fatal injuries because if your brain stops working then you cannot experience anything, so disrupting the processes that keep it going (cellular respiration, homeostasis, excretion, eating, blood pumping, etc.) and just about anything can kill you from starvation, blunt trauma, freezing, disease, cancer, etc. negligible senescence does not cause your cells to regenerate so much as it causes your cells not to run out of telomeres which once broken down cause cell death and other afflictions. You would also accumulate lots of scars over time, likely develop cancer somewhere, or catch a fatal disease. You would also be likely to go through lots of surgery, have to take lots of medicine to combat the diseases you have to constantly fight, you would lose limbs and they would not regrow because our bodies don't do that, and any loved ones could still die leaving you to suffer on in misery for much longer. Once everyone had immortality people would begin to reproduce all the time, after all there are plentiful resources out there now in terms of food, and thus the population would explode, then we would run into food shortage and people would starve to death because you cannot function without food. This reproduction would also fail to kill off stupid and genetically defunct people and so you will have growing parts of the population that harbor ideas and ignorance that will cause systematic collapse.