I guess I should preface my comments with the fact that I'm a physician who works in Geriatric Medicine.
We definitely choose interventions based on individual's goals and desired, informed by the risk/benefit of the intervention along with the individual's pre-existing frailty, medical status, and life expectancy. There are healthy and functionally well 80-year olds who absolutely benefit from ongoing preventative medicine. There are severely frail 70 year olds with multimorbidity who would not benefit from the same approach as the above 80 year-old. Age is just a number (to a point).
With the above said - our society and our medical institutions do a terrible job talking about death as a natural part of life. We (the medical system) are also terrible at having hard conversations with families when things are changing. As a result, many older adults spend the last year or two of their life in a pattern of acute decline, incomplete recovery, tenuous stability, and acute decline (again). Many of these individuals are dependent on others (or are institutionalized) with some degree of cognitive decline.
If you look at qualitative data, only a small minority of people wish to extend life at all costs. Most people weigh out quality of life with the net benefit of an intervention and the hardship of going through that intervention, and come up with an answer which usually isn't "do everything doc".
Society also has a poor understanding of how beneficial our interventions actually are in advanced multi-organ disease and our medical system does a terrible job explaining. Many of the tests we do and interventions we choose have marginal clinical benefit.
I guess the TLDR is that I'm not against offering treatment to older adults, and certainly don't suggest people should "give up and die", but I do strongly feel we massively overuse resources (which has a huge negative societal impact) to provide marginal benefits to frail older adults who likely wouldn't choose the above treatment if someone actually sat down with them and had a real discussion.
n.b the dichotomy of "giving up" and "fighting" when it comes to healthcare is commonly used, and I believe a harmful way of looking at care.