I think you're a bit quick to declare something impossible just because it seems unlikely or counter-intuitive.
Yeah. For example, how about some sort of monitoring device that tells you when it's optimal to chill out in the woods.
A tech start-up that would encourage a balanced lifestyle and create more digital downtime? It does sound paradoxical.. however, I am currently developing a start-up right now that will literally move (physically and emotionally) you offline. Never say never. :)