I don't know why anyone thinks this will happen. You can obviously write anything you want (we have an entire realm of works in this area that everyone knows about, fiction) and yet huge amounts of people believe passed around stories either from bad or faked media sources or entirely unsourced.
I'm not saying either you or the parent commenter is right or wrong, but fiction in books and movies are clearly fiction and we consume it as such. You are right that some people have been making up fake stories and others (the more naive) have been quick to believe in those false stories. The difference now is that it's not just text invented and written by a human, which takes time and dedication. Now it's done in a second. On top of that it's easy to enhance the text with realistic photos, audio and video. It becomes much more convincing. And this material is created in a few seconds or minutes.
It's hard to know what to believe if you get a phone call with the voice of your child or colleague, and your "child"/"colleague" replies within milliseconds in a convincing way.
I agree it's fundamentally different in application which I think will have a large impact (just like targeted advertising with optimisation vs billboards), but my point is that given people know you can just write anything and yet misinformation is abound - I don't see how knowing that you can fake any picture or video or sound leading to a situation where everyone just stops believing them.
I think unfortunately it will massively lower the trust of actual real videos and images, because someone can dismiss them with little thought.