Scientists we saw in Fallout 2 were US Army, the United States Chemical Corps, headed by Lt. Colonel Charles Curling. So what your saying is that Eden is in charge because there are no civilians left, just the Army?
In some ways yes. That and he is part of COG.
EDIT: Isn't the President Commander in Chief of the Armed Forces?
Yes. That is the point, the President of the United States cannot be an active service member/general because that would give them complete and utter control of the Armed forces (doesn't mean much in the Enclave but thats the beauty of the Irony).
The President must be a civilian because there must be a civilian commander in chief, to sum it up.
EDIT II: I agree with Okie, Eden gained sentience, he's a computer and has no right to be a US Citizen, let alone a Presidential Advisor. Before he was alive he was a number crunching machine, surely one was on the Oil Rig, how does a ZAX get to be Secretary of whatever?
Prehaps he doesn't have a right to be a real-life American citizen. That much we can agree on. But in the world of Fallout? Who are we to say a computer can't be an advisor/citizen?
Keep in mind, Eden was created to serve as an ABSOLUTE last resort President. When all viable options (that follow succession Protocols) are gone, and that happened with Fallout 2.
Edit: Im not asking you all to like him or follow him to your deaths (hell we Americans fight over our presidents all the time) but I would ask you to (grudingly) at least admit there is some cause for his legitimacy as President.