So as much as eliminating the problems of old age would be a huge win, there are two things that really make me hesitate to endorse it:
Plank's Principle "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it ..." widespread immortality would mean that senior respected scientists would maintain their extremely respected position, and would potentially stifle any progress as their reputations were sunk into existing paradigms. The strongest voices in the community would have a permanent vested interest in already existing. Hopefully eliminating aging would also eliminate the tendency to calcify in one's beliefs, but the reputational reasons to not change their minds would persist regardless.
The indefinite perpetualization of existing dictatorships. Succession is when dictatorship is at its weakest, since the new ruler doesn't have the legitimacy that the previous regime did; with immortality, dictators would be able to maintain their position indefinitely.