I always thought it was dumb for them to assume the audience is dumb.
Well, the audience usually
is dumb, but there's also practical storytelling considerations to take into account. If one were to be realistic and have the Earth government involved as well as a potential Earth based military force, it could have taken up valuable storytelling time just getting all that exposition out there. In the end, a streamlined approach is the best one.
Here's the Federation President, he makes calls all shots on the civilian end on Earth. Here's a Starfleet Admiral, he calls all the shots in Starfleet, and wants the President out of the way. Eventually a state of emergency is declared, with Starfleet officers patrolling the streets. There, that's done, move along with the story.
As opposed to:
Here's the Federation President, he makes calls all shots on the civilian end for the Federation. Here's a Starfleet Admiral, he calls all the shots in Starfleet, and wants the President out of the way. But wait, there's also a Prime Minister of Earth, the Federation President can't make a ruling for Earth without consulitng with him. And so, even once the Admiral has taken out the President, he won't really have any power, since the Earth Prime Minister is calling the shots and won't recognize the authority of an Admiral who has just ousted a President. And what about the state of emergency? Shouldn't Starfleet colloborate with Earth's own military? See, this is just getting unnecessarily complicated. Remember, there's only 90 minutes to tell this story.