It's not just animation, American TV historically tended towards episodic. Other than the daytime soapies (with their "plots" you could still follow if you missed 6 months of episodes), you had sitcoms, police procedural shows, sci-fi adventure etc, which were all very episodic, but might have some character plot threads weaving through. There was a mid 90's crime show called "Murder One" which would followed a single case for many episodes. This was so far outside American expectations that the show, whilst getting rave reviews for great acting, great writing and stories, failed to get enough viewers to keep it going. So, you had a number of earlier American shows that attempted to have more of an ongoing plot, and doing it excellently, but failing to get viewers.
It was about when Arrested Development came out that things started to change. That was very unusual at the time both for the ongoing plotlines and the lack of a laugh-track. Back then the laugh track was a strict genre signifier: no laughter robots = drama, laughter robots = comedy. It was so universal, that even though I've seen a huge proportion of the US comedy shows dating back to the 50's and 60's, Arrested Development freaked me out because it didn't have a laugh track. This just wasn't done at all before it since the dawn of television. You had to have the laugh track (and episodic plots). Arrested Development changed all of that, so it's only really been 10 years since this sort of comedy has been acceptable on American TV.
There are some older sci-fi shows that almost qualify, but almost all of those follow a Monster of the Week format, or at the best you get 2-part stories so that they can throw a cliffhanger in. Dr Who, which would usually have 4 part stories ... there really wasn't anything comparable from America, so it's not "The West", it's specifically American TV. So, American cartoons being so episodic, is really just an extension of how TV has traditionally been done in the USA.