I might be misremembering but I didn’t think they brought in Martin Sheen as a late addition. They always wanted the president to be in it and to be played by a big name actor (several were considered - I remember reading that Sidney Poitier and Alan Alda were others) but the original idea was that he’d be a distant figure, included as a recurring character who might only appear every few episodes. Sheen’s casting as Bartlet wasn’t inconsistent with Sam being the central character. The show was meant to be about the White House staffers and the way Bartlet was treated in the pilot (talked about a lot but only appearing in that one scene at the end) was meant to be the norm.

The change was the decision to then promote Bartlet to a main character who appeared in every (or nearly every) episode and effectively become the nearest thing to a ‘main’ character for much of the its run.

they needed someone to actually play “the president” instead of just have the staff talk about him all the time

Funny, because Veep managed to do this so seamlessly. But then Veep was about the bureaucrats being self-obsessed greedy hacks clawing at the coat tails of power, rather than Model UN nerds bemoaning the imperfections of everyone outside their White House clique.

One could skirt around the President by focusing on the petty bureaucracy and political fiefdoms that divide Veep’s staff from their kingpin. The other absolutely had to introduce this Messiah-like figure for the staff to alternately evangelize and and debate and betray.

Him leaving wasn’t exactly a loss anyways.

No, but only because they were all so interchangeable. Lowe crafted a role for himself that was identical to all the other sanctimonious Aaron Sorkin clones bouncing around the set. It wasn’t until you got guys like Alan Alda popping in to do a Bernie Sanders impression that they had anyone to really argue with. Even then, most of the show was about pushing past Labor Democrats and cutting deals with Rockafeller Republicans, which was basically just the Clinton Era without the sex.

During the Bush Administration, The West Wing was just an opportunity to retcon how cool 90s-era DLC Democrats were. And a guy like Rob Lowe was just the wrong kind of fit for a show that worshiped anyone other than Rob Lowe.