Yeah that's totally understandable. I'm not advocating for removing/demoting major media stuff or bumping up obscure sites, not even saying anything about the scoring algorithm should change.
Rather I think obscure sites should get more opportunities to be organically upvoted on (and if they don't get voted up, then fine) and not just fall off /new after a few hours only to be seen by a few people. The BigCo stuff naturally gets posted often several (different) links from different people, whereas obscure stuff is only posted by a single person once. So this is about evening the odds.
One idea here could be to have some set of guidelines for a domain like: is not commercial, is not promoting something, has had past HN front page discussions. Then those domains could just have a slightly different color in the new stream.
Maybe better would be to weight the first 50 votes or so, so if the site has rarely been submitted to HN, every 2 votes count as 3 or whatever variable weight works. The problem is that you can't give blanket +1 votes to submissions from less mainstream sites either, so initial traction might be harder to achieve anyway. I don't know if mods manually upvote some of the new content with this in mind, but yeah, in the end this second chance pool is pretty equivalent.
Rather I think obscure sites should get more opportunities to be organically upvoted on (and if they don't get voted up, then fine) and not just fall off /new after a few hours only to be seen by a few people. The BigCo stuff naturally gets posted often several (different) links from different people, whereas obscure stuff is only posted by a single person once. So this is about evening the odds.