Reviewing your questions to consider, it's very hard for me to conceptualize a show that fits the description in your title. Most of Star Trek is heading down to the planet of the week. Given the choice between focusing on the away team and focusing on the crew operating the starship, I think I'd sooner follow the away team and consign the ship crew to being nameless extras.

What's interesting, though, is that I can think of at least two occasions where the people making Star Trek had similar doubts to the ones you've articulated here. First, when Roddenberry decided that sending the captain down was too dangerous, which led to the development of Riker as a character. Second, when the Enterprise writing staff decided that what Star Trek really needed were marines and came up with the MACOs.

So, while I can't really envision a Star Trek where the main cast is confined to the ship, I can envision a Star Trek where a starship's senior staff is distinct from a starship's MACO command staff and the main cast is split between the two.

In other words, we're talking about a version of TNG where Riker, Yar, and Worf are not Starfleet officers, but MACO officers. In this version of TNG, away missions are composite affairs: Geordi is still heading down if there's an engineering problem to solve, Crusher is still heading down to respond to a medical emergency, and Data is still heading down in case they need to win $12.5m playing craps. But Lt. Col. Riker is still in command of the the away mission and Capt. Worf is bringing up the rear.

The thing is, this changes the texture of your average away team-centric episode so little that all we've really done is... add marines to Star Trek. This will inevitably pull Star Trek in a militaristic direction and I don't think we've gained anything in exchange.

Closing thought. While writing this response I encountered something that surprised me: Major Hayes is only in five episodes of Enterprise. I suppose it's a credit to Culp's performance that I would have guessed he was in at least ten episodes had you put me on the spot and asked, but on the other hand, it's pretty telling that even though Enterprise kept the MACOs through season 4, they just became redshirts and the Enterprise writers never even bothered to tell us who their new commander was.

It's hard to imagine Lt. Col. Riker faring any better given the same constraints. You can give the Enterprise a MarDet, but if you're going to give them something to do on a regular basis that isn't equally or better suited for the senior staff, then you're writing a far more action oriented show than we're accustomed do.