That is not necessarily a flaw. One of the players I had in mind to captain in my upcoming campaign does not want “to decide everything”. They’re the captain in a Traveller campaign they play in and told me that ever too often all eyes were on them to drive action. I don’t see this risk in the players of our group, yet see that one sometimes wants to lean back and let others make decisions. This is where away missions and supporting characters come in.
It also mitigates the hierarchy-problem. Since Captains should not go on away missions, too often, they’re the natural choice to play with a supporting character every other scene. Since supporting characters have rank-restrictions, this will also turn upside down the hierarchy.
Which is what I would do with any NPC captain.
I, too, think that formal hierarchies offer a tremendous amount of potential drama. Yet, players have to be self-reflected enough to allow this to play out. I’m adamant that my players are, yet some, sadly, do not seem to fully trust themselves.
Anyway, you can play Star Trek without the formal hierarchy among the players. I already mentioned play at Starfleet Academy, where every player is a cadet and, thus, holding the same rank and privilege. You can also think of a “lower decks” setting with all the characters being ensigns and lieutenants etc. Also, “outranking” is defined by your definition of the chain of command – which can be very different and does not necessarily include command authority of a Lieutenant over an Ensign.
With regard to Star Trek Experience, I’d say basic knowledge of Star Trek suffices. There’s nothing wrong with the casual good advice from the GM’s side, if things go too awry.