That's a really good point. The obvious solution would be to say that the narrator is simply writing the story for their own benefit and not for anyone else to read, but that's not usually how it comes across. I don't have a solution, but if you're looking for a catchy name for this effect, how about "Midas's Barber Syndrome"?

There's also a negative image of this, for an example of which (simply because it's handy) I'll give you the opening to my 2006 book, The Lurkers:

I may not have much time to write this. The Gates of Memory are shutting all around the town. I’ve been trying not to think about it, trying not to draw attention to myself, but I have to face the facts. Today, while I still know what the facts are. In a few days I may pick up this notebook and not recognize a word I’ve written. The Lurkers can do that, you know. I’ve seen it happen.

And you?

You’ll think it’s just a story.

There's no end of fun to be had with this stuff.