This is how AI will integrate into Dnd, probably in this order.
1) The more advanced random generator. Able to create specific npcs or magic items, or descriptions of random places. This is where ChatGPT is now. You could also use it to create art for specific monsters.
2) Combat Assistant: The combat side of the game is fairly rigid compared to a lot of other more free-form elements. You can probably have the AI roll dice, have it run NPCs and monsters, and do a pretty solid job with some DM oversight.
3) DM with a human on the wheel. The AI takes over DMing, but a human has the ability to override it when it goes off the rails a bit.
4) Fully autonomous DM.
Now for people thinking chatGPT is still just a "dumb robot", you aren't paying attention. These thing has exploded in sophistication in the last few years, and its passing turing tests in certain areas left and right. Sure its not a novelist, but it absolutely can right things as well as bog standard humans can. And that's just now. Give it a few more years of tuning and sophistication, and suddenly its the top of the high school class. A bit more, best college writing graduate. And a bit more after that, it surpasses human writing entirely.
What people underestimate is the speed of progress. This is an exponential curve, and the snowball is starting to roll down the hill. Its going to pick up speed fast.
Maybe AI will advance quickly, maybe not. What we call AI are better described as exprt systems. They mimic intelligence and can absorb patterns and spit out variations of the pattern.
What they are not, what still be decades (perhaps a century) away, is actual intelligence.
They are getting better at mimicking intelligence. That doesn't mean that they think or that the approach will ever lead to true intelligence.