Earlier quoted context omitted.
It can work the other way, too. Your offspring may be more likely to survive if you stop consuming resources once they become viable.
Are you sure that availability of resources was a limiting factor during a large part of human evolution? ie what has driven human population growth - a fundamental change in availability of natural resources or a fundamental change in how humans exploited them? I'd argue it's the latter, and that's driven by accumulated knowledge - and before writing - the key repository of that was - old people.
Part of the reason it benefited us that some but not all people become old is because people require more attention during two phases of their lives. Our biological evolution has prioritized care for the very young over the very old, with respect to a limit on resources (like attention), effectively until the modern age. In some cultures, for instance, those with teeth must pre-chew food for those without, or expected members to engage in ritual suicide at a certain age.