First of all, I get what you're saying about how one's particular reason for participation in the forum will affect which method of reading the forum will be preferred. You've made it clear that your primary reason for participation is moderation and that that affects your choice of methods. I think (and here I am guessing) that this means you have to see all the new threads as they come in - to see if each new post is offensive and/or spammy. I can understand that - but of course, that's not *my* main objective.
That said, here's what I don't like about "New posts" (as implemented in the "Prosilver" skin). It doesn't remove things from the list once I've read them. Instead, they stay on the list and when you hover over the little circle next to the thread title, two things indicate that there is "nothing new; nothing to see here":
1) The color is black (instead of red)
2) The "hover" message says "No new responses on this thread" (or something like that - don't have exact wording in front of me)
Well, it seems pretty obvious to me that if there's nothing new in the thread, it should be taking up space on the page. Based on the general design of Usenet newsreaders, the general idea is to not show you things that you've already read.
That said, here's the problem I have with saying "Well, it's there - just look under the 'hamburger' menu and ...". Yes, it is - at least in Prosilver. But I had to hunt around (and post to this thread looking for help) to find it. That took time, and most people won't do it. That's the basics of UI design - if you hide something under a menu, most people will never find it (unless they take the time to ask around and be led to it by more knowledgeable people - which, again, most people won't do).
And, as Peter O posted earlier, it is twice as much work - it is move, click, move, click instead of just move, click.
Finally, note that (as far as I can tell - and admitedly I haven't spent the many hours it would take to fully investigate and document it all) there isn't a "hamburger menu" in either of the skins whose name begins with an R. I could only find the "hamburger menu" (and, thus, the "Unread messages" click) on the "Prosilver" theme. If I am wrong about this, by all means let me know, so that I can try out the "R" skins some more (since I do generally like their look better than the "Prosilver" skin).
If this post appears in the wrong forums category, my apologies.