Linkrot is a real problem, but it's nowhere near as harmful as PageRank was.
Once links have commercial value, people don't want to give them away for free. Serious publishers quit making links to outside sites and soon other people got out of the linking habit.
This problem has been solved 7 years ago. In 2005, Google introduced nofollow:
<a href="..." rel="nofollow">...</a>
I believe that nofollow was mainly introduced to fight against guest book spam, so links in comments wouldn't be accounted by the PageRank algorithm, thus removing the incentive for that nasty spam.
However, you can also use nofollow to link to your competitors without increasing their page rank.
that's indirection and psychological warefare on the part of Google.
in the big picture you give them data and they process it as they wish; "nofollow" is just a suggestion. for instance, they can compute metrics of it such as the ratio of follow/nofollow links pointing to a site and feed it into their scoring system
good links do get passed around in comments (this is the blog post you really should read about this) that shouldn't be nofollowed, while other webmasters are stingy and nofollow everything they link. so who knows what Google or bing does with this.
What is clear is that if you play it safe and give no link, Google won't give them any credit.
I don't think page rank really plays as much of a role as the fact that it is easier to replace a webpage than to remodel it. See the "More" button at the bottom of this page.
Once links have commercial value, people don't want to give them away for free. Serious publishers quit making links to outside sites and soon other people got out of the linking habit.