The upper quote was post number seven of this thread, apparently you missed it.
No, I didn't.
They would be the ones who beam down, they would be the ship's trouble shooters, they would be the focus of the show, they would undertake missions...
So either they're a team of Mary Sues (perfect for every job) or the show focuses only on what this tiny complement of officers and enlisted crew can handle. So taking the wide open range of options of plots based on a wandering starship and limiting it to the specialties of these four people, plus or minus a guest of the week.
Without the crime aspect, I imagine the show being like NCIS or CSI in that there would be a situation that the team would be assigned to. Exploration, or a investigation, or potential combat, or initial meet and greets of new civilization (like a advance party). Maybe they would even investigate a crime too.
Right. So first contact, which is generally the Captain's or the First Officer's domain, but we're hand-waving it to be in this group's dossier. So, a big old hand-wave to bring something into their purview that they shouldn't be doing that's really someone else's job but is just too exciting to pass up.
So the whole ship is here at this planet doing... something else. But the show follows these four doing their thing. Which happens to not only somehow be the most important thing going on (but somehow they're not the department heads) and is just by coincidence the most exciting thing happening during this mission (otherwise the audience would want to focus on where the action is).
After a few episodes you either have these four as hands down the most experienced officers on the ship and they're promoted out of the show's premise (below decks / lower ranks), or you're just hand-waving all logic away, again. But whatever. So there's a ship-wide mission, but we're focused here, with these people. It would be really hard to make whatever it is they're doing the most interesting aspect of the entire crew week-after-week. Unless, again, we're just hand-waving.
If invaders gets on board they would be in the thick of it.
So hand-wave it, again. Either the invaders just magically happen to beam in where these people are, or they're suddenly all security officers... who're the ones that would be called in to repel a boarding party.
And all during these events, the captain would stay on the bridge where he belongs.
Picard generally did that in TNG.
And the forth member of the team is a petty officer (2nd class), a non-Human male in his mid twenties. Engineering and technology expert. Has a husband and wife on the ship.
It would be great to see more "non-standard" relationships in general, and in Trek specifically.