Interesting trivia: The main protagonist of the series was suppose to be.... Sam Seaborn. You picked up on the clue in the first episode. The President wasn't supposed to be in every episode or scene. He was initially planned for 3~5 short scenes every year, however with the out of the ballpark effort that Sheen did, they had no choice to keep him very involved. Part of the reason why [SPOILER REDACTED] is that while the rest of the cast recieved significant raises in Season 2 and when it came time for [SPOILER] to recieve their raise the studio/network were unwilling to give them the raise. It did not help that they were largely written out of the 3~5 major conflicts (President vs Mrs Bartlett, Josh vs Donna, Toby vs Congresswoman Wyatt, Zoe vs Charley, President vs Leo).
Do you listen to The West Wing weekly podcast? They're just at the end of S1 and I chuckle when they talk about not spoiling future episodes. I think "who hasn't seen the West Wing??!" But there is probably a whole generation of people who didn't see it when it was on NBC. Or Bravo. It's my go to television when nothing is on and I just want to relax. I can't tell you how many times I wake up on the couch and the Netflix screen says "ARE YOU STILL WATCHING THE WEST WING" I need a Tell-a-Donna right now!