Indeed. From a biological standpoint, it's important to realize that an indefinite lifespan, as a life history trait [1], does not confer evolutionary fitness. The fact is that organisms do not appear to evolve to a maximal lifespan — they evolve to an optimal lifespan. Humans are already considered to be K-selected [2], and increasing lifespan appears to necessarily decrease fitness in other areas, as has been seen in worms [3] and flies [4] (e.g. reproductive fitness decreases and age of maturity increases, when lifespan increases).
More importantly, "near-infinite" lifespans reduce the efficacy of natural selection — longer-living organisms evolve at a slower rate. While, perhaps, unappealing, the culling of species members well past reproductive age is necessary to allow for more resources and potential for competition and selection in their offspring. And humans are certainly still undergoing natural selection in many arenas; just look at sickle cell trait [5] or or CCR5-Δ32 [6].
Death is a feature, not a bug.
[1] https://en.wikipedia.org/wiki/Life_history_theory
[2] https://en.wikipedia.org/wiki/R/K_selection_theory
[3] http://www.ncbi.nlm.nih.gov/pubmed/8608934
[4] http://www.ncbi.nlm.nih.gov/pubmed/25601460