I think I've taken a liking to short hair on girls in recent years. Also, humans don't have hair only on their heads.
Anyway, hair was originally for warmth and protection, which is why it grew EVERYWHERE. I think your scarring theory is plausible, but only in the event that damage is incurred. As humans evolved, we gained an increasing amount of 'bare' skin - skin capable of sweat. This was vital for our ancestors to herd/chase prey, as hairy men would overheat to rapidly in such a pursuit.
I heard someone talking on the radio once, about how he and some friends tried to chase down some deer. Initially, their plan was just to charge ahead and pursue the target in a single direction. Obviously, this didn't work, because deer are much faster than humans. Another issue they encountered was that the target deer would switch herds when two groups came near and intermixed, making it very difficult to track. Eventually, the plan these folks devised was to position a man or two at the top or just beyond the top of each hill in a given area. By yelling, they would alert one another when the herd was approaching, and the men would scare the deer back into the center of the area. At this point, they could theoretically move in with spears and make several kills, as the deer were somewhat trapped.
So yeah, less hair means better cooling systems. Hair still exists on the head because of the brain, most obviously, and on the other place because of, well, Darwin. As far as military intimidation, I would say that a shaved head loaded with tattoos and piercings and other strange things would send the message that they eat their young, and would like to eat yours as well. It's like how moths have spots that look like eyes - humans probably recognized this on some level, and found a way to copy it.
Dinosaurs went extinct primarily because a catastrophic climate change that destroyed most of the food supply. Volcanoes and asteroids aside, there were other issues. Firstly, the Dinos were irrationally large, which was impractical in many ways. Most obviously would be the herbivores - Elephants are the largest land mammals presently, and they are rather large herbivores. Dinosaur herbivores grew to many times the size of modern elephants, traveled in groups, and left hundreds of house-sized piles of dung all over the place. This encouraged diseases and parasites, and all around poor health. Large Dinos were on their way out one way or another.
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When I allow it to be
There's no control over me
I have my fears
But they do not have me