This proposal goes against all the efforts to replace shortened URLs with their true destination.
Also, it becomes the moderators' responsibility to clean up link rot (by changing the bookmark) instead of the community's (by editing). I am not a moderator, but I am opposed to putting further burdens on them.
EDIT in response to OP's comments
Ok, so you could avoid the link-shortener issue by still showing the true URL. But I don't think this proposal meets the test of a useful new feature for a site like SO. I think about this by asking myself a few questions.
- What problem does this solve? Linkrot - and only linkrot.
- Are there any other tools to solve the same problem? Editing, which we can also do to improve posts in other ways. Advantage to just editing.
- What advantages does this proposed solution have over existing solutions (editing)? If a broken link is found, all instances of that link are fixed at the same time.
- Is this advantage material? That depends on whether links that break are likely to have been cited multiple times. I have no idea if there is a database-querying way to work this out, but I suspect the answer is "no". Linkrot is more likely on less-common links, rather than frequently cited links such as documentation to particular languages or products. So most of the time, editing one post will probably fix the problem for that broken link. As noted below, I expect there is a power law distribution in number of times a URL is linked to, so in most cases, a given URL only receives one or two links.
- Who would have to do the work if this solution were introduced? In the proposal, moderators and/or high-rep users would be responsible for changing the bookmark - other users would not be able to merely edit that post. So the work would be concentrated on a small group who already have a lot to do.
So in summary, instead of all users editing broken links as they find them, only a small proportion of users would have to either find and redirect the broken links, or deal with a user flag requesting the link to be fixed. Given that there is probably a power law distribution of links from the site, most destination URLs will only appear once or twice and a simple edit will fix up a broken link. This concentrates work on a smaller group for a small material benefit.
Making it a user choice to put a link in the database or not would make things worse: first, we have to decide something (more cognitive load); second, broken links would then have to be dealt with two different waves.
Further on the cognitive load issue, I do not think it is a good idea to encourage the community to edit posts to improve them, and then make that not work for linkrot - possibly only for certain URLs! That would just be confusing.