Yes, but I'm not saying they should fix the New page. The New page has too many garbage submissions for me to want to spend time there. But if they fixed pages 2-4 behind the front page, I would visit those pages. Those pages have more signal-to-noise than the New page, so I want to read them. And if those pages were getting upvotes, maybe their stories would make it to the front page.
I click more. I find the stories that I am interested in. I open the submission in a new tab and the comments in a new tab. I repeat this until I get to page 4.
I read an article. I upvote it if needed. I read the comments page. I then refresh the page before making any comments. Once i've finished reading and voting and commenting i close the pages and move to the next article.
I use a method similar to the described by DanBC, but I open the comment page in a new tab and I immediately open the submission from that tab, because it’s easier to hit the back button than to remember where each story came from.
Fixing the new page is relatively easy, and it could free more closures to the other pages, so it increase the time that the links live before expiring.
I also sometimes use the “filtered 2+ new page”: http://hnapp.com/filter/d3a308f2ac9a071c0bf174e0c1a8fd22 , i.e. someone else thought that it is interesting. It’s not so painful and it’s also good for days where a single new saturate the front page.