I'm a big fan of finding the simple solution in things. Part of it is searching for elegance. Part is my thesis that most complex things can be distilled to 1-2 levers that really impact 80% of the situation. But what happens when there really isn't a perceived simple solution?
That can happen when the situation isn't fully well developed. There's simply not enough transparency and information out in the open for there to be a perceived simple solution.
Military strategists call this the fog of war. Information, misinformation, and lack of information accumulates, and complexity increases. The perceived simple solution is hidden by cognitive overload. Decision making is paralyzed.
One solution is to accelerate the situation so that information is apparent. For me the fastest way to do this is to talk to as many people as possible; I did something similar when [I first moved back to Asia.] (http://www.taklo.co/my-100-day-plan/)
Another way is to establish a time limit on when a decision has to be made. What this essentially does is work backwards from the end, and forces an individual to cognitively let go of the fact they don't have enough information, and thus have to come up with the most simple solution they can given constraints.
Sometimes a simple elegant answer isn't the answer. Sometimes the answer is to get your hands dirty and just finish the job.