It can definitely solve problems that exist. I've been using it near religiously for the past 6-7 years as the home of my GTD system, as well as a general store for archived reference information, and the design of their product fits my needs perfectly. That said, the flexibility in use that's one of its main strengths is also one of its greatest challenges, since it can be very difficult to pick it up and get the most out of it.
I've heard that point of view a lot, but it's definitely not me. In fact, if I had to pick one word to describe it, it'd probably be "liberating". I don't have to hold anything in my brain anymore, so when I'm relaxing, I can relax 100%. Don't have to worry about forgetting anything, because I know it's all in there. And when I'm ready to 'get something done', as it were, some things to do are right there. I love it. That said, it did take a while to get set up and used to.
I might be missing something, but it feels like it's trying to solve a problem I don't have. In fact, it feels like a problem that doesn't even exist.