Interesting you mention Marvin Lewis since he is the last remaining perennial loser coaching an NFL team. He has little respect from those above him AND below him, which is sad since he is a great defensive mind, but not even LeBeau was able to generate wins in Cincinnati.
Cowher was the antithesis of what you were driving at as far as even-tempered, he got in people's faces shouted (and spat) but he was a great motivator and a fundamentals football coach (Football 101
)
A lot of coaches are like a lot of players, they are divas, self-serving selfish and single-minded, who appear to us cold, calloused, and unapproachable.
For every 20 guys who can take being screamed at there's 1 or 2 who can't. Buck up Haynesworth, you're a grown man and you're making bank, so what if a little dude gets in your face (1 example)
Some players can't make the mental transition. This could be nothing but a rumor BUT word around the 412 regarding Limas Sweed's injury inactive for the last few games was because he was in Western Psyche.
There's a lot of stress for some in this line of work, money or not.