Yeah, there are downsides to everything, the question is whether pros > cons.
Imagine tomorrow, some mystical cosmic event made it impossible for people to die of natural causes. Would you institute a law that once someone made it to 100 years old, they should be executed? This would prevent most of the downsides curing death would spring.
I think the answer to this is obviously no, that would be completely foolish, if not immoral. But when we start with the status quo of death existing, puzzlingly, most people think death is a good thing.