301 Redirecting broken links worth it?

I have seen some people offering broken links 301 redirects on reputable sites. Do you think it is worth it? (Given it is contextual of course and NOT random)

I'd take such a link (if it's in my niche).

Yes. All internal links should immediately resolve with a 200 status code. Any URLs that are updated should have all of their links updated to reflect the new URL, not just redirected.but Are we talking links in the top-level navigation? Or a bunch of in-content links throughout the site?
If it's just a bunch of in-content links scattered throughout the site, I wouldn't say "don't do it." But I would ask, "do you have anything better to do?"

You should cleanup from time to time, yes.
If I clean 301 redirects I do it in 2 steps. First I evaluate in the logfiles whether these links are still visited at all. Then I would check if the redirecting page has backlinks that are valuable to me. If users/googlebots no longer visit the redirects and they don't help my link building I remove the redirects for cleanliness/to reduce the error rate. For large website-moves I leave redirects for at least 1 year before I take the exam as described as a rule of thumb.

301s on broken links can be solid if they're relevant and the domain authority is there. Done right, it's a clever way to reclaim 'link juice' and improve UX.