We have something that does this, but it's not optimal. When activated, the system will routinely send
HEAD requests in an extremely polite manner, and put anything that doesn't come back with a HTTP 200 response into a queue for users to check, as well as notifying the author of the post about a broken link.
In theory, this should work well, in reality it doesn't. When a considerable amount of context for a post depends on an external resource and that resource goes away, it can be very difficult to find a replacement for it - fixing it often means just rewriting the post. The Internet Archive's Wayback Machine helps, if you can find a copy of the resource at the time the post was written. If it's not there, and the answer isn't useful any longer without a working link, you're looking at a lot of work or deleting the post if it's no longer of use.
Wayback does have an API and we experimented with automating this to some extent. We can ask the archive if it has a given resource, and the dates of the snapshots it has available. If it has a copy, and a snapshot in reasonably close proximity to the date the post was written then it's likely a good match. But, this just prolongs a semi-broken state - what happens if the archive no longer has that resource one day? It doesn't fix the underlying issue. It also needs human supervision.
Posts that people actually care about are generally well-maintained, even when it comes to link rot. What the automated system tends to churn are links on stuff that hasn't been viewed in a long time, and the effort required to fix this stuff is generally more than the value of the stuff being fixed. That's why we didn't continue putting it in a queue for folks to work on, it just piles up, there are few 'easy' fixes, and it takes time that could be given to more important content.
tl;dr; - the suggested edit system is actually a better fit for this as people find things opportunistically and fix them. It's clear signal that someone found something, found it useful, and made sure it remained useful for others. In other words, content that at least someone still cares about.
Tasking people to fix a link to a bug report surrounding an ancient version of some language that has long fallen out of relevancy is just not an ideal use of anyone's time.
That said, I do want to experiment with it some more, as time permits. Squelching alerts on everything under a certain amount of recent views would drop a pretty big chunk of noise. I won't say that link rot isn't a problem, but there are more pressing and important ones to tackle first.