As Edward Tufte says, "Correlation is not causation but it sure is a hint." That increased strength improves life expectancy should be the null hypothesis. At least at the one end, extreme frailty is a common eye test for poor health. Since this isn't a scientific journal here, but a discussion, I think most of us would agree that stronger people often have more resources to ward off disease, cope with temporary reductions in nutrient bioavailability longer, can defend themselves from threats more easily, and can avoid more dangerous falls by maintaining their center of balance. And that's not a comprehensive list.
Personally, I'm satisfied that increased strength reduces all cause mortality and I believe the link is strong enough to be actionable now. I'm an evangelist for it among my older friends and relatives. One way strength reduces deaths is by preventing common injuries, e.g., falling and breaking a hip. A recent study showed that a simple graded test of sitting on the ground to standing could differentiate mortality risk sharply. While we can't measure how much strength and how many years it adds, not least because that's just a vague question, the link here was almost an order of magnitude from the lowest grade to the highest grade for one repetition of standing from the ground.
http://www.cbsnews.com/8301-204_162-57559095/sitting-and-sta...
http://cpr.sagepub.com/content/early/2012/12/10/204748731247...