Hello! Sorry for not posting in a while. It might be a while before I post again.
Most political dramas have fictional presidents. Although the obvious reason for this is that events need to diverge from reality or that celebrities should not be impersonated, fictional presidents can also make a story more timeless by not providing an obvious frame of reference. (Of course, some movies based on true stories may feature an impersonation of the current president, as do comedy shows. There are now so many fictional U.S. presidents that Wikipedia has a 10-part list of them. These presidents range from comical idiots to fellows you might want as president even if you're happy with the current occupant. However, as with any fictional world, there must be some divergence from our own world. (This doesn't count pure sci-fi and fantasy films which may resemble our world but be utterly different, or works that happen in the future). Usually, most fictional stories do not alter the world around them very much. It is not that hard to accept that the events of, say, Planes, Trains, and Automobiles happened in our world as nothing in said movie would make the news and pretty much everywhere corresponds to a real place. In my view, the amount of consistency with the real world starts to become strained when fictional companies appear, as the presence of these companies might alter the everyday lives of Americans. Stories dealing with a fictional President, however, have no apprehensions of dealing with our universe as the plot must be unpredictable. Despite this, these shows must deal with current political issues and reference political history, and therein lies the problem. For example, Jed Bartlet of The West Wing (a show I haven't watched), one of the most famous fictional presidents, was supposedly Governor of New Hampshire before becoming president. However, Bartlet's fictional term overlaps those of Steve Merill and Jeanne Shaheen, altering their political careers, and all the fictional senators and former presidents would replace their real-world counterparts. Given this seismic shift in political history, it seems unlikely that the issues would be anywhere close to the issues today. And that doesn't even get into the alternate genealogical implications of Bartlet being descended from his namesake, Josiah Bartlett....