If the old links were just kind of hanging around the news page, without anything to suggest that they're specifically relevent to the moment, it would be hard for them to attract the kind of time-focused attention that you would get from a freshly-posted item. You could probably get by with a "featured classic link" that changes every day or so to keep people interested, but that would be more of a small feature or gimmick than a new type of site. Trying to push it much more than that would, I suspect, thin out the commenters too much, killing the ability to have back-and-forth conversations and turning it into more of a bookmark site.
There's a place for collecting good, old links, but news sites are for news. I think trying to force both ideas into one site would feel too awkward to work well.
(But by all means, prove me wrong. I thought Twitter was stupid, too.)