Can reduced cognitive load lead to some kind of mental or physical "atrophy"? Muscles, if you don't use them, degenerate. Everyone who has had a broken leg in a cast for a few weeks and then seen the thin stick that reemerged once the cast was removed, can attest to that fact.

But does the same happen to the brain? Does mental ability or brain matter atrophy, if life is to easy for us because all the products we use are so highly usable that we don't have to think anymore?
Assuming you're getting at a related idea to your other recent question (Does a more ergonomic and user friendly interface/device make the human brain work less?), I wouldn't worry about user friendliness causing mental atrophy by precluding the need for thought. Thought continues well beyond matters of control to matters of application and optimization. (E.g., can I use my washing machine on AstroTurf? How much high-efficiency detergent do I really need? Can I still use the old stuff?) When systems work particularly well together, entirely new areas of thought may emerge (e.g., the Industrial Revolution and the Italian Renaissance depended largely on the stability and prosperity of their host societies).

However, the "use-it-or-lose-it" principle may apply to specific skills and even general abilities and physical senses to some extent. Secondary language proficiency is one such popularly recognized example. I'd also recommend checking out the Scientific American Frontiers miniseries, Changing Your Mind (some episodes are available on YouTube). One particular episode with which I'm familiar features a research participant wearing a blindfold for a long period of time, during or after which a neuroimaging method (probably fMRI, but I can't quite remember) shows activity in her visual cortex when she's processing tactile stimuli. These sort of repurposing processes probably occur naturally throughout neurological development, especially in youth when neuroplasticity is greatest. AFAIK, neurological models of learning and development in general describe a lot of processes involving pruning of unused connections and reinforcement of frequently used connections. Others here probably know a lot more about these topics than I do, but it seems clear enough even to me that to some extent, atrophy is a natural and even adaptive part of the learning process. Even without referring to neurological substrates, one can argue that learning often involves the process of elimination, so the atrophy of ideas representing eliminated possibilities (e.g., the world is flat?) is desirable in some ways.

Of course, not all atrophy is desirable, and not all results in adaptive repurposing of the relevant brain structures. My former doctoral advisor once told me a particularly disturbing story about the punishment of one of the assassins of Archduke Franz Ferdinand, whose death played a role in sparking the first World War. I've looked into it a bit since, and suspect the story is apocryphal, but it's interesting nonetheless. Supposedly the assassin was locked away in a completely dark cell for so long that he went blind. If, as I suspect, this is mere apocrypha, I don't know whether this can happen in general, but the loss of vision in subterranean species of fish, lizards, and insects is well-documented in evolutionary theory.