I don't argue with people needlessly, but I do try and see all perspectives.
Even if a view is wrong, understanding where it's coming from can help you in persuading people who hold that view.
Playing devil's advocate is also a way to anticipate a counter argument to your own. I tend to do it mentally because of that, and I can sometimes know what point someone will present before they say it. Sometimes, I can come up with a better argument for them in my head than they are actually making .
I also find that playing devil's advocate can create compassion for someone who is not on your side. It promotes tolerance and basic human respect for people who don't hold your views. I think it's important to view things from a human perspective, which involves emotion and personal experience and not just look at black and white facts. Playing devil's advocate is essentially putting yourself in the shoes of someone who's coming from a very different place, even if it doesn't change the "facts".