I think the real dead end is making websites for both mobile and desktop. They are simply too different to ever have any real hope of producing something that translates well to both without hopelessly crippling one of them.
Mobile-only sites, sure. Desktop-only sites, why not. If you want both, do both instead of making a hideous web design Cronenberg pleading for the relief of death.
Back when mobile exploded I got a bee in my bonnet that I had to have an app for my website. I spent a couple thousand dollars to have a highly recommended mobile website designer do this for me. The result was HORRIBLE and I decided to just live with what I had. Turns out my native website on mobile looks GREAT, far better than on a computer screen. Go figure.
I find that responsive design works well for simpler webpages. But for more complex pages or apps, yeah: it totally falls apart.
However... whenever I see an app or site that has two separate websites, I know I'm in for trouble: sometimes one version will miss some features, and I'll invariably have to request the desktop website. The worst of them was my previous health insurance provider, that only had one very important feature in the mobile version.
Mobile-only sites, sure. Desktop-only sites, why not. If you want both, do both instead of making a hideous web design Cronenberg pleading for the relief of death.