After careful consideration I have come up with my best guess as to why Ferguson acted as he did (in no particular order).
1. Contempt for the rebels. As a career officer from a fairly prominent family Ferguson probably felt contempt and personal arrogance towards his enemy, (esp. the overmountain men) whom he regarded as "Barbarians", "the dregs of mankind", "a set of mongrels" and "banditti". This is in response to atrocities committed on local loyalists. Given his prior experience, he probably didn't respect their fighting ability or speed as much as he should.
2. Timing. It seems that Ferguson thought he had more space between himself and the enemy. I believe that he never intended to fight at King's Mountain, but he chose the high, defensible, location in case he was attacked before reinforcements arrived. Although he did feel he could hold the position if attacked.
This would explain the lack of any defensive construction. Ferguson was very smart, well educated, experienced and had years of formal military training in strategy. His lack of preparation or a well thought out strategy (not to mention his reportedly amorous escapades the night before) leads me to believe he was caught completely by surprise.
3. The location. As a trained and capable tactician, Ferguson would understand the importance of the high ground in a defensive position. However, I think if he knew he would be attacked he would have chosen a spot that was harder to surround and had a way of escape. Also, given his ability and interest in arms, I find it hard to believe that he would not have known the tendency of shooting too high when facing an enemy from higher ground. Perhaps he thought that the terrain would help his bayonet equipped troops.
After seeing the battlefield, I think Ferguson felt that the land was too steep (on three sides) for an enemy to effectively assault and that if he was attacked he would be protected by the elevation and would only have to defend an assault from one direction.
Finally, Ferguson probably couldn't foresee how ineffective a bayonet charge would be on such steep, forested terrain. A bayonet charge is pretty worthless if it isn't coordinated and is disastrous if it doesn't "break" the enemy. Given the terrain, coordination and support for a charge seems impossible.
4. Overconfidence in his men. While I don't feel Ferguson underestimated his opponents (else he might have been on the offensive), I do feel he overestimated his force at least to the point where he didn't act like he was about to make his "last stand" (see #3).
5. Failure to adapt during the battle. Whether it was arrogance, pride, or inflexibility, once he was surrounded and assaulted, Ferguson didn't fight a defensive engagement, which would seem to be the most sensible given the terrain. I would think that after the failed bayonet charge he would have considered a change in tactics. Also, Ferguson did not try to "break out" in force and retreat. This may not have been possible, but it couldn't have been any worse.
To sum it up, I think Ferguson being attacked with surprise lead to his indefensible defensive position and that the terrain probably had the biggest impact on the battle.
While a well respected and capable officer, Ferguson's lack of preparation is inexcusable.
A few questions for you:
1. Was the top of the mountain too small to afford protection to Ferguson's men? i.e. was the entire mountain top under fire from the encircling enemy? If is wasn't, could Ferguson "circled the wagons"? (the next time I'm there I'm going to send someone to the center of the top with a red coat and see if the are visible from every direction)
2. If he could have avoided fire from below and waited for the enemy to reach the top before firing or charging, could he have won? Or at least held out for a few days?
3. Why wasn't he more informed on the position and intentions of the enemy. Is this arrogance or incompetence?