Some folks find combo edges harder to sharpen when using sharpening stones (same reason others don't like recurved edges). A Spyderco Sharpmaker solves that problem by getting "in between" the teeth of the combo edge.
Some folks don't like combo edges for some of the other reasons mentioned above: aesthetic reasons, not enough either edge, etc.
Personally, I do like them. I find they cut plastic reinforcing straps easily where a standard edge would just "skate" right off. They also cut zip ties without any fuss.
I have knives with different sorts of edges: plain, combo, and serrated only. When I am preparing food, I prefer the plain edge. The exception to that is when I am slicing some hard crusty bread. That's when I pull out the serrated bread knife.
I find that when I am cutting man-made materials, such as blister packs or cardboard boxes with plastic straps, combo edges or serrated edges work better for me.