That's an overly simplistic model. The factors leading to your demise are interrelated in a complex way. Diet (including sweeteners) can affect your weight and diabetes risk, which can affect a number of downstream morbidities (heart disease, kidney disease, cancer), any of which can be the one to take you out.

A quip from Adam Eget on one of Norm Macdonald's podcasts: A lot of things would have to go very right for me to end up dying from too much salt.