The Dream Of A Left Winger
The series is the result of left-leaning writers thinking of their ideal political team and then thinking about how they would really act in political crises. Here's the thing, they probably already have a choice of politicians they might vote for but what they are interested in is the perfect choice. They aren't thinking about the politics, they are thinking about the characters' great personal qualities: dignity, intellect, a strong sense of principles. These characteristics are the dividing line between the good and bad guys. If they want to show that "Hey, we don't think all Republicans are bad" they will show them as dignified, intelligent and with a strong sense of principles e.g. Ainsley Hayes.
Why then do they end up as Fox News Liberals
and Blonde Republican Sex Kittens
? Because the first set of good guys are Democrats, so if somebody wants to stick around for a long time without going over to the dark side, they have to start lining up with the President.
"The first set of good guys" or more importantly the first batch of viewers. The basis of the show draws in viewers of a certain bent and favourable characters have to be favourable to them.
They had to fit in the entire political landscape
The show had to focus and develop one team of characters but also explore the entire political landscape that they worked in. All of those ancilliary characters wouldn't get much type to portray their personality and their politics so very often they had to be boiled down to a single view point. One had to look at the (literally) crusty old guy who said "If there are thousands of guns out there, I want my wife and my daughter to have one" and say "Got it! Conservative Southern Democrat, likes guns, won't like Bartlet".
It was an auteur piece
Look at the first few seasons and see how many times it isn't a "Written by" or "Story by" Aaron Sorkin episode. The answer is very few. This resulted in a very consistent feel across the board. The dialogue for each character was in a consistent style, a character arc could be developed for one of the main characters and plotted out at a good pace. However when he left, it dropped them in it and before that there would have been more of a chance of any trope prefixed with Author appearing.