Well, part of how they work affects certain enzymes and chemicals in the body that stop or reduce inflammation (duh!), and, somewhat unsurprisingly, inflammation although a problem at times, for example, a sore knee, is also part of our general human adaptation to life, in other words, it is how we have evolved.
Pain is one of the most common reasons for a patient seeking medical advice. It also plays a major role in the progress of all sorts of diseases and conditions, in other words, sometimes the pain is the thing, and at other times it is an outcome of the thing.
You might have seen that a common theme to the three causes is pressure and, given that we walk upright, this pressure is greater than say a dog, you do get oedematous dogs, just less, commonly than humans.