Incidentally, those aren't the most basic can openers; it's possible to make a can opener with no moving parts. Search for "swiss army knife can opener" to see some pictures.

Personally, I first learned to use the simpler design; when I saw the kind with the gears and handle, it seemed over-engineered to me. I find them equally easy to use, but I've seen the handles break on the more complicated kind (they were plastic, not metal) and I've also seen the gears go out of alignment. Yet the simpler design is rarely seen except in swiss army knives and military rations. This seems to support the idea that some added complexity can be worthwhile for most users as long as the product is otherwise well-designed and well-built.