A lot of first person classics use journalism as the main POV, so in those cases it does matter how good of a writer the narrator is. On a similar note, if I were to write from the first person POV of a street thug, who never read a book in his life, and I sounded very literate, obviously this would make little sense.
Since when do journalists have to be good writers? I was a journalist my whole life pretty much. Journalism really has little to do with writing, or maybe I should say that your writing is not the most important thing in journalism. Anyway, that probably doesn't matter. I know a lot of journalist write memoirs, but I was thinking more about fiction than journalism when I started this thread. As to your second point, I don't know why you are bringing a thug into this. But sometimes it really is amazing what writers can make work.
Look. Go to the DMV, I don't care where. Pick out an average person and tell them to write a memoir. I don't care if they make the entire story up. Most likely, it's going to be a very, very, poor read.
I'm trying to say, when you read one of these classics, where the story is told from a journal, and then it turns out the narrator has some writing experience, it makes sense.
I think writers make for interesting characters because they can be perceptive, deep thinkers and even naive. Stories don't have to be about a writer and his writing, but about a writer and his life which can offer a whole wide range of experiences and reactions. The overthinking writer The emotionally unstable writer The shy recluse writer The overconfident writer The 'well is dry' writer The writer obsessed with a muse Etc etc. Writing doesn't have to be the focal point of the writer story, but the experiences that shape the writer's worldview -- which will obviously shape him -- offer some good opportunities for storytelling.