That simplifies just about any economic system, which takes a lot of the complicated stuff out of government and class hierarchies.

Right, but they very clearly don't get all of their food out of a replicator, nor do they use the holodeck for things like hair cuts. There is still people who serve as cooks, waitresses, barbers, etc despite the technology being there to not need those jobs.

And that's what I want explored in more depth.

I’m a casual Trekkie, but I don’t recall much detail about the Federation’s or Earth’s government structure. Do people still vote? Is it a benevolent military dictatorship? Who knows? And who cares?

I've been dipping my toe in the books. At least in the first book for PIC, The Last Best Hope, they very clearly still have political struggles for power, corruption, tribalism, and voting. It ain't a dictatorship, but the goals and views of the government leaders aren't wholey benevolent.

A particularly good example was the Federation council member Olivia Quest. She's a rep from a border planet, whos been facing some issues with the romulan star going supernova, and all the immigrants that are mayhaps being sent their way. So she raises a big stink over any and all help towards the romulans. It's self serving, selfish, and tribalism, but she was voted in and she wasn't alone.

All of this is very familiar to real life. But it's the exact kind of details I want, but on one of the shows. They made it interesting in the books, they could just as easily make it interesting in the show.

That’s the very core of the entire franchise and I’m fine leaving it that way, unscrutinized, since it clearly doesn’t hold up to scrutiny.

Maybe the tech of replicators/transporters/holodecks should be left unscrutinized, because ultimately it relies on technobable for it to be compatible with a suspension of disbelief. But I don't think the same goes for the societal structures of the federation. It worked in the Last Best Hope, I think it could work on the screen.