Soldiers without will or skill are what you want. They're going to get stupid ideas in their head (no skill) but they're not going to actually act on any of them (no will). They're perfect for unskilled labor and generic work.
The soldiers with will and no skill are no different from enemy saboteurs. They're going to get stupid ideas in their head (no skill) and they ARE going to act on it (will). One example would be an officer in Battlefield 3 deciding to do a surprise attack on an enemy force that was significantly larger and better equipped. Due to their stupidity and ladderclimbing urges, they appealed to their men's sense of duty and camaraderie to get them to go through with the attack. The end result of this was a total wipeout of his own unit. There are so many different disasters that can happen just by having a stupid guy that is willing to act on their stupid ideas. Incorrect retreats, diverting equipment from other fronts, falling for feints or disinformation, etc.
The disasters don't have to be limited to combat either. Imagine a stupid officer decides that destroying a dam upriver of the enemy is a brilliant way to wipe them out. They also happen to forget that all of that water will still flow downriver and wipe out several of their own camps. Another example could be an officer who is stationed in the middle of nowhere deciding to tunnel through a mountain to create a shorter route. So they order a ton of explosives, wood, steel, and workers that could've been better spent elsewhere on their dead end project. Now let's also add that they cut corners with hiring engineers and wound up with bad people who severely misjudged the scope of the project... and now all the workers and equipment are trapped in a cave-in. Oops.