I went into this thread ready to give an opinion about how useless I though Jaresh-Inyo is as a Federation President, but all this discussion about governments has left me very confused.
While watching Homefront/Paradise lost, I kind of assumed that earth had no government of it's own and was governed entirely by the federation government. This is because Leyton came to J-I to approve the tightening of security on earth only.
If you pay attention to the dialogue, though, Leyton makes it clear that, at first, he's talking about tightening security at
Federation and
Starfleet facilities on Earth, not at all public locations throughout the planet. It's the equivalent of the Chief of Naval Operations attempting to persuade the U.S. President to tighten security at federal offices and Naval installations. Even if there's a local government, it doesn't affect them.
Only later does Leyton attempt to persuade President Jaresh-Inyo to declare a state of emergency on Earth and put Federation troops on every street corner. But it's a well-established practice in federal systems for the federal government to have the authority to declare a state of emergency in a province or locality without needing to obtain that province's or locality's government first. U.S. President George W. Bush didn't need Louisiana Governor Kathleen Blanco's permission to declare a state of emergency after Hurricane Katrina -- in fact, Governor Blanco declared her own separate, Louisiana declaration of a state of emergency.
If there is an earth government, I think he would only need this government to approve security measures on earth and would only need to go to J-I to approve security measures for all federation planets, as he is the president of the federation, not of earth.
Again, no. He'd need the Federation President's authorization to tighten security at Federation government installations and at Starfleet bases. To make a comparison, if the Chief of Naval Operations wanted to tighten security at federal and Naval installations in Virginia, he wouldn't go to Virginia Governor Bob McDonnell -- Governor McDonnell has no authority over security at the Pentagon or at Norfolk Naval Base, even though both are in the Commonwealth of Virginia.
And, as I demonstrated above, a federal government doesn't need permission from the provincial government to declare a state of emergency in that province.
And, remember, part of Leyton's plan was to get the entire Federation government scared and on edge so that they'd accept him once he usurped power from the President.