For the general continuity hawks, Friedman has his own set of Earth political leaders, not related to those of preceding novels/fanfic/RPG nor later referenced in the ENT RW books. But we can argue that the Friedman "President Littlejohn of the United Earth" could exist in parallel with the ENT "Prime Minister Samuels of the UE" - plenty of governments today have both a President and a Prime Minister at the top of the executive power structure.
FWIW, in my native Finland, we used to have a powerful executive President like the US or French ones, with a puppet Prime Minister, but once we got rid of an annoying president-for-almost-life who really overstayed his welcome, everybody agreed on gradually stripping the President of his or her powers until we've reached a situation where the President is ceremonial (much as in, say, Germany or Switzerland) and the Prime Minister holds the executive power under strong parliamentary control (in the classic British fashion). The next logical step would be to drop the President concept altogether - which may have happened to United Earth after the Romulan War.
Or then the UE retains the President position, but it's symbolic and ignored and unrelated to the decisionmaking that takes place in the novels dealing with Earth.
For the record, the most recent ENT novel, The Romulan War: To Brave the Storm, features United Earth President Lydia Littlejohn alongside United Earth Prime Minister Nathan Samuels. Given that the Prime Minister has been depicted as the real leader of United Earth throughout the war, it's pretty clear that United Earth has a system like Finland's, Germany's, Ireland's, etc. -- a mostly ceremonial President and a Prime Minister that does the actual leading of the state. There's also a sequence where the United Earth Parliament is depicted as making an important decision that the Prime Minister must adhere to, so there's the implication that it's a PM who serves with Parliament's confidence.
I find that concept both horrifying and unnecessary. First off, nothing in "Homefront"/"Paradise Lost" in any way contradicts the idea of United Earth continuing to have its own government and its own President. Two, what you're describing would mean that United Earth would be denied its own government and its own ability to run its internal affairs -- a situation equivalent to that of the District of Columbia in the United States, which has historically alternated from being denied its own government at all (instead being governed by a Congressional committee no one actually wanted to serve on) to having a local government whose decisions Congress can override at whim. Given how undemocratic and oppressive that situation is, I can't imagine an enlightened Federation would endorse it.Or, even, the UE President position is blended into the UFP President one, depriving Earth of a "true" head of state but OTOH giving it symbolic access to the very highest seat of power (which would in turn fit well with what we see in "Homefront"/"Paradise Lost").
In any event, several novels and short stories, including "Eleven Hours Out" from Tales of the Dominion War, have established that the United Earth government continues to exist into the 2370s, with the United Earth Prime Minister joining the Federation President and President of the United States of America in touring the Breen-ravaged San Francisco after their attack.
The main incompatibilities in the Friedman novel are as follows:What else is "wrong" about the Friedman book?
- Its depiction of Earth technology as being much less advanced than ENT canonically established it to be
- Its depiction of there being no United Earth Starfleet
- Its depiction of T'Pau as already being an aged and well-respected Vulcan leader, rather than a relatively young recent revolutionary
- Its depiction of the Daedalus-class as being a new kind of starship; the ENT novels make it clear that the Daedalus-class is already a bit older as of 2156
- Its depiction of the number of the Federation's founding worlds is much more expansive than what the ENT novels and the other modern TrekLit novels have established (that the UFP was founded only by the states of Earth, Vulcan, Andor, Tellar, and Alpha Centauri)