As a parent my guess would be that people see it as a way to introduce welcome variety and whimsy into the daily routine of reading a bedtime story. While also feeling like you're using a hobby interest to help with a real practical issue.
I have a small library of children's books and we've read them all several times, the good ones many times.
That said, I wouldn't personally turn to these language models. From what I've seen they tend to generate rather bland and boring stories. I would rather make up my own or reread "Kackel i grönsakslandet" for the hundredth time.
For kids story writing I've been getting better results with 3.5 at times.
Where 4 is way better af coding.