The more important reason is that it's hard to do programmatically. For every link, you'd want to link to the most recent, active archive entry. As far as I know, this isn't easy to determine.
Have you ever had the experience of going to archive.org, plugging in a url, and seeing that the most recent one is actually dead, but then you can go back in time and find what you're after?
It's easy to say "Well, that's ok. Take me to the dead link, and I'll go back myself." Maybe. But with Dan's exacting standards, I somehow don't think that'll pass muster.
The ultimate reason this probably won't happen, though, is because people can do it themselves. It's not hard to copy the link and visit archive.org. Every other link (past, flag, hide, favorite) is there because it's hard to do.
EDIT: On the other hand, https://news.ycombinator.com/item?id=30384630 shows a way it could be done. I didn't know about the date wildcard feature.
Out of about ten links I clicked, I think there was only one that still worked. All the rest I had to run through the IA, whose homepage takes 5 seconds to load enough for the search box to show up, then wait for it to load the captures, and finally wait for it to fetch one of the captures. A direct link would be very welcome.
The addition should be easy, no need to query the IA site or anything because IA will find the nearest date to the request automatically iirc. Something like one week after the submission would allow post-submission updates without being likely to show a 404 capture.
(By the way, the question I ended up picking for our applicant was: "what did you like or dislike about the culture in previous places you've worked at or interned?" It went over well and I got some insight into what they'd expect (or enjoy) when joining the team. The colleague I did the interview with later said it was a good question :).)