Hmmm - it is extremely difficult to prise my 9 year old grandson away from his tablet or any other screen based device for the time it takes for him to eat his dinner.
I know what you mean, on all counts of what you said above, not just this point, but I would say that AI content in a form deliverable to children is pretty straightforward. You just need to present it right - as a story, an immersive game, or as a TV series acted out by humans or a story teller in the theatre or at school. I have no doubt at all that quite soon the AI machines will output AI drama in the form of films and tv programmes. The rate of progress is exponentially rapid.
Right now - as you say - some models produce risible attempts at fiction, but all you need do is train them on fiction. These models I have downloaded are not trained to write fiction - others are. You can ask my model that I used above to tell you all about stellar nucleosynthesis - I have done and it knows all about it, or you can ask it a range of difficult questions about the origin of earth's water - was it here when earth formed or was it delivered by comets and asteroids crashing into the proto-earth. It will tell you all about it and discuss the different isotropic nature of the oxygen in comet water and that from asteroids and then it will come to a conclusion based on the isotopic content of earth's present day water. It knows all about all of that stuff. If these models are designed to write film scripts, that is what they will do. You just need to let them see as many of them as you can find.
Also - if you want a passable story, you have to give the right sort of prompt, but you are certainly right - some of them are absolutely dire. they were not trained for that job. The same thing would be true if you asked you car mechanic to write a story, I expect. It is not what he is about. If you find a different individual with a different sort of training, you will get a different result.
I think the fact that last year the Hollywood screen writers guild went on strike about the use of AI, might give a clue to which way the wind is blowing on this subject. Not that most of their output is anything to write home about. I can scan Netflix for half an hour and not find ANYTHING I can bear to watch.
