I use Liferea, and am mostly happy with it. The "Mark Items Read" button in the toolbar needs to go away, I agree about that.
The "Unread items" folder already went away for me. It was never useful for me, so I just deleted it. I click on "Next unread" to go to the next unread item. This moves to the next folder with unread stuff, if necessary. I've rarely had trouble finding an item if I click on the "Next unread" button too many times, but I can see how that could happen.