I think there are a lot of reasons to scoff at the "but death saves money" argument. Most of those reasons have to do with the difficulty of accounting for the value of a life fully lived.
E.g., if a highly educated worker dies ten years before retirement, how much productive labor did the society that educated that person lose out on?
What about the non-paid labor that the elderly/retired often take on? "Free" child care for the grand kids, much higher rates of volunteering in churches/schools/etc., and so on.
Suffice it to say that this is not exactly a trivial computation...