Read the bit you quote please dude lol. I didn't say anything about the quality of writing in shows, did I? That's all you.
I said "even mediocre" for a reason. People who think LLMs output anything worthwhile, creative writing-wise don't even know what mediocre writing looks like, let alone good writing. Most of them don't even recognise bad writing as bad.
No LLM is capable of writing anything extended at all that doesn't turn immediately into drivel, or anything even very short that is even mediocre. This is not going to change, because it is inherent to the way LLMs (as opposed to theoretical GP AIs) function.
They cannot understand context.
The cannot understand relationships between people or objects.
They cannot understand social values.
They cannot understand punchlines (nor humour as a concept, but this is where it shows up most).
This will not change.
Because they are Large Language Models. They are not thinking machines. They are put-one-word-in-front-of-another machines. People - including very senior Hollywood people are making category errors about what they are.
You are making a category error about what they are - you say you "know the limitations" but also claim "we are just at the beginning". No. That's a tautology. If you think we're "just at the beginning" of what LLMs can do in terms of creative writing, you are mistaken. You do not understand the limitations. We might be "just at the beginning" of AI in general (I'd say that was actually the 1970s, myself), but but it's GP AI which will make the difference with anything genuinely creative. It will also probably be terrifying.
And "give impetus to the technology", dude, what? How fast do you think tech moves? How many years do you think this stuff even was in the making? You think they're going to make shocking strides in LLMs in what, a month? 3 months? 6 at the outside? Absolutely they will not. In fact the discussions of LLMs show that if anything, they're basically stalled for at least a while - the large ones anyway (smaller, more specialized ones are making some headway, but they're not for creative writing). The strikes will be over, one way or another, for a very long time before even improvements in LLMs become evident.
Also, no, it doesn't "just need a bit of polishing and refining" if you use an LLM to create dialogue. They output complete drivel. Stuff that's worse than a blank page for an actual writer. That's just slew of cliches and obvious tropes in a row, but without any feeling, any real sense of who the characters are (because it can't think - though it can say have two generic archetypes and use bland, cliched lines for both), without any wit, without any intentional humour and so on. Don't confuse essentially using an LLM instead of rolling on a few charts to come up with a backstory for an NPC or details for a town or something with writing dialogue or detailed plots (and you must have detailed plots for shows, they're not RPGs) with writing a TV show.
Now, let's be clear - I'm just talking about for creative writing. LLMs have incredible potential for other fields, for good and ill. Just not for creative writing.