Hehe - the story of your horse being used in rodeo comps made me laugh. The all-around horse that I showed on the QH circuit for years (top 10 in nation high point eq) would buck so hard that my trainer and other people who had witnessed his antics would try every year to make me enter the local rodeo as they figured they would win money off of me, thinking that if I could stay on him I could stay on anything.
Personally, I think the best all-around horses, and esp WP horses, are actually quite spirited. In order to really move properly, they can't be of that completely dead-head attitude. I still remember watching the girl who won the reserve world champ in amy WP a couple of years ago get bucked off by her "quiet" WP horse the night before the finals. Didn't affect her any in the class.