I can understand an international CT force made up of NATO members, but a private yet government created/sponsored counterterrorism company/agency? Plus the fact that the Emir was obviously bin Laden.
Plausible deniability, perhaps, if the Company was "private" rather than officially government? Changing an obvious OBL into "the Emir" was done so that the character didn't become dated, like Prince Charles in Patriot Games did.
I will say he also ruined politics for me. I would absolutely love someone like Jack as president, but we will never have someone like that get far enough in our politics to actually get there.
Jack DIDN'T get anywhere in politics. He became President because of multiple catastrophes, and was re-elected due to terrible (as in terribly clumsy) opposition after he literally saves every voter's life, by his actions against the (first) Plague. The situation that would be equivalent would be the post Civil War period, where the main qualification for Grant and the next few presidents was that they were successful generals, not politicians.