In D&D 3.5 there was a skill called "Tumble" and its only purpose was to do exactly as you are describing. Pathfinder lumped it in with acrobatics when it was streamlining its skill list. I really wish they would mention it elsewhere in the rules, because otherwise it seems like they forgot that they kept tumbling through squares.
The reason it's not encouraged for every AOO is because it would grind everyone's movement to a standstill, and in a game like pathfinder the last thing you want is for people's turns to be padded out longer.