Because I can't feel the buttons with my thumb and have to look down, unlock my phone, switch to the right app, and then tap. It's a horrible experience.
Or when you want to pause said movie because you're getting a call, which prevents you from pausing the movie. Happens to me all the time while Chromecasting.
I use a wireless Xbox One S controller as a shield remote. It works great; I also use it when streaming games from my PC to the TV. I tried the shield controller and was pretty unimpressed.