These are two great but very different questions.
Let me address the second question first. A staged photo can be authentic depending on context. Think of something like a picture of an entire sports team all standing in a row. It isn't natural or common for them to all stand in a row (especially with all of their uniforms clean), but there's nothing inauthentic about it. All you're doing is documenting all the members of a team or class. Prom photos are staged, as are graduation pictures. They are authentic documents of specific moments. Wedding photos are staged. However, staging a photo in a non-ritual or documentary fashion can be quite inauthentic. For example, if you dress someone in clothing they never wore, clothes that gave a false impression (like gang colors), that would be wrong.
Now, the artistic question. The advantages of a single still photo are focus and composition. The very motion of a film creates possible distractions. Action draws the eye, as do many things that might distract from your purpose. (Think of something like the classic "wardrobe malfunction." )
You can compose a still photo with compete control, focusing it on crucial elements that tell a precise story.