Phones can do (almost) anything. That's if you allow for a bit of flexibility with the meaning of the word anything, of course.
Phones can talk. Write. Sing you a song. Answer your questions. Do the dishes (if you have a smart appliance.) Reply to your emails. Organize your life. Or disorganize it. Find your keys. Pay your bills. And so on and so forth.
But... can you make a serious video using only a phone?
The question is not whether smartphones are a serious video and filmmaking tool, but why on earth you would disagree that they are? [source]
Here's an example of a whole feature film shot on iPhones.
The point is: you can do it too. Get started. Now!