It is not all about heart disease or cancer. For example, I know some perfectly thin people with debilitating arthritis. A chronic disease need not be fatal or even life-shortening in order to make your aged years unbearable.
Eating well and exercising enough pushes all sorts of problems a decade or two away, I know it pretty well. But that still does not mean that the last quarter or so of your life will be OK.
The intended target of anti-aging is precisely this part of lifespan that sadly cannot be called healthspan.