How do academics deal with growing old?

All people deal with getting old(er) in some way, but I can think of a few aspects that are unique to academics.

One way to keep up the performance is to gradually shift from hands-on work to advisory work. It is clear that an aging professor can't keep up with the hours invested, enthusiasm, desire to prove oneself, etc. of a PhD student or junior faculty. However, our older guy has participated in a lot of academic craft (writing papers/grants, advising, doing research, reviewing, etc.) over the years, which can give a significant edge to junior people around him. Guiding others can and does produce scientific breakthroughs even though the senior professor didn't think it all up by himself. Further, it also educates the next generation of researches which also an important and challenging job.

People outside of academia are usually obligated (with exceptions, of course) to retire at a given age. On the other hand, a professor has the possibility to attain the emeritus rank, which lets him be an active member of the academic community theoretically until the end of his life. This partially offsets the time investment of PhD studies, postdocs, etc., if the argument is that people in academia have fewer "productive years" as opposed to people who start off right after undergraduate.

Finally, professors are usually respected members of their communities, so even if some of them perform less in their later career, there are always other duties they can excel at. For example, focus on teaching or department duties or writing books.

In my opinion, none of these options is inferior to the "pure research" track and I feel that many come naturally as personal development. In other words, I don't think aging professors find it necessary to outright compete with their younger colleagues, but rather mature into other roles that benefit the academic community.

There are a number of ways senior academics have their careers shift, and some assumptions in your question aren't necessarily valid.

In most jobs these don't matter that much since one doesn't need to be the best, and "good enough" is good enough.

You're asserting this isn't true for academia without much evidence. There are plenty of professors who settle into modest but respectable careers, teaching a few courses, having one or two long-term grants, etc.

However, academia is unique because it lives and dies on ideas.

I don't think this is unique to academia, and you don't just need a volume of ideas. You need the ability to execute on those ideas, and experience helps with this - indeed, experience may help filter ideas that seem promising but are likely dead ends, unproductive, etc.

Even if your volume of ideas declines with age, as long as you still have some over a threshold of "I have nothing to work on now", it might not matter.

Without ideas, there is no funding proposal, and with no funding proposal, there is no money, no students, and no job.

Senior researchers, with established labs and track records, have an easier time getting funded, not a harder time.

This sounds like a very difficult situation for academics: they grow less and less able to come up with good ideas, but still have to compete with the legion of younger researchers at the peak of their mental capabilities all coming up with ideas. Furthermore, younger researchers are also in better shape physically, and can put more energy into their work.

How do academics deal with growing old in a job where growing old directly impacts one's ability to perform?

Even if all your assertions are true, their careers aren't over. They may become chairs or deans, identifying, recruiting and mentoring those "legions of younger researchers". They may use their prestige and reputation to bring those younger voices into their projects, either as members of their labs, collaborators, etc. Or, in many cases, they take a step back and focus more on the trajectory of the field as a whole, thinking about slightly broader and grander ideas where the perspective of someone who has been working on the same thing for decades is valuable.

As (not entirely facetious, at all!) counterpoint to the other answers and comments:

Clearly, "getting older" (whatever this means precisely) is construed as a bad thing, with mostly bad side-effects, by the question, and as an under-current in the answers, even if they push back slightly.

As in my earlier comment, it might be interesting to reflect on the reversed assumptions and corresponding question: "How can young people have any hope of doing meaningful research, being adequate scholars, and competing in the academic marketplace, when they are so immature, inexperienced, ignorant, and naive?"

(I would seriously claim that, although the previous is presently a rhetorical question, it reflects enough reality to bring the question above to more-or-less a "dead heat", I think.)

That is, population X may reasonably imagine (if they are optimistic) that the traits they imagine that they have are exactly what makes them superior (in some useful sense) to other tribes/populations/clans, and can have discussions about how those other populations (purportedly lacking these signal distinctions) can bear their own existence, survive at all, etc.

I've heard all too many times the idea that (in math) "well, when you get old-and-tired and can't do research any more, you can always teach". Toooo many assumptions here, especially that people who lack the energy or interest to continue research "can always" teach. E.g., I'd claim that if they were not good teachers before, loss of energy and interest wouldn't help... (Of course, such comments are in a mythological context where "anyone can teach", but "only the special ones can do research"...)

It is true that in current contexts there is an aggressive identification of "research" with "funding" and "entrepreneurial spin-offs" and "technology transfer". I cannot speak for engineering departments and such, but this is clearly not the model of all departments in universities. Some departments are caught in the middle, e.g., mathematics, where there is a seductive possibility of playing short-term, big-money games (as opposed to small-money, quiet, long-term scholarly games).

I do not claim to understand the arc of personal scholarship, nor the gamut of "economies" of grants and such across disciplines, but it is relatively clear in my experience that there are many scenarios where I'd be very much more interested in hearing a scholarly opinion from a decades-long experience than from a glib newcomer. Sure, newcomer rebels can be interesting, but the context is complicated.

So, my facetious-rhetorical response is "What? I'm getting older?" (Sincere!) And, then, "Wait, what, all this time I thought I was finally figuring out how to do stuff, I'm being declared ever-more-incompetent?!?!"

:)