When we tested a variant of this idea, we found that it didn't work for what I guess you could call psychological reasons: readers reacted negatively, even violently, to seeing junk on HN's front page. By "junk" I mean stories that were placed there randomly and that weren't of high-enough quality to otherwise be credible candidates for the front page. Basically, it was an "ow my eyes", "get that shit away from me" effect. (I don't mean to demean the submissions people posted that got randomly placed in this way; it's just that words like junk and shit reflect how users reacted to the random placement thing.)
HN users have an intense emotional relationship with the front page. This shows up in the inevitable "How is this on HN?" comments when a story somehow violates the commenter's personal contract or mental model of HN. Randomly placing candidate stories on the front page created a version of this that was a lot worse. It violated people's model of what HN is supposed to be, in ways that the randomness exacerbated. Two lessons I drew from that experience: (1) people's relationship with HN is surprisingly personal; and (2) never jeopardize that bond. Runner-up lesson: don't introduce noise into an emotional relationship.
If we had software that could measure how credible an article is as a candidate for HN's front page, I'd be willing to try this again. But I suspect that would amount to software that could measure how good an article is, and that would be the P=NP of internet news sites.
I'm still convinced that a lot of the best content—i.e. submissions that would gratify intellectual curiosity and that the community would have a great time reading and discussing—languishes in obscurity in the lower echelons of /newest, so HN's front page is still far from optimal. The second-chance process has helped (https://news.ycombinator.com/item?id=11662380) but I'm convinced that there are more things that we can do, mainly by building ways for the community to do them. It's important that we not build new mechanisms that just reproduce the upvote system, though.