Unfortunately it's in my opinion conceptually impossible to replicate the Star Trek experience in MMO form for two reasons.
1. The chain of command means only one captain per ship. This means getting people to accept being in what could be considered something of a pyramid scheme, in where the later you join the game the harder it becomes to be a captain, as the older chain engineers and tactical officers become captains themselves. More likely, everyone is a captain, and therefore... the essential experience of the star ship is lost.
2. Even if you did have an affective chain of command, the realities of real life would make it impossible to manage a ship effectively. The captain may be sleeping, at school or at work when the Romulans attack or the ship gets pulled into some crazy wormhole. In star trek, the captain lives on the ship and can therefore respond to unexpected events. And what if you're logged off on the ship, and your ship then explodes? Do you log in dead, or in outerspace?
What would be great, is a Star Trek MMO-like single player game. Something along the lines of Oblivian, set in the Star Trek universe - wherein you can start off in the academy or as an ensign and work your way up to captain or even higher - and the world could immerse you inside the crew. They could then make that game multiplayer... where you have a save file that specifically requires all the people who started the game to be online together to continue it. Or an online world where you can take your single player or co-op players into a persistant world and fight rival factions for fun - but there are no missions.