The main reason an actor needs to learn about status is to be able to make scenes realistic. When the characters don't have a status relationship, a scene looks wooden and fake.
BTW, playing high status is not necessarily better. People who relentlessly play high status in every situation are commonly called "assholes". (Usually behind their backs.)
I'm not saying that you have to consciously play status ("decide to play"). I'm saying that when you interact with someone else, you are playing a certain level of status in relation to them, whether you are aware of it or not.
Engaging in some phony behavior will, of course, make people perceive you as a phony, with all the loss of respect that that entails. Respect, of course, is a big part of status. When you don't respect someone, you tend to play higher status toward them.