I agree. Of all the bands that have impacted what we call "emo", Jimmy Eat World has probably done the most.
On a different note, I feel like someone dropped the ball in not having Weezer on this list.
Jimmy Eat World to me is just an universally loved band. They have rock songs, ballads, emo jams, and even very artistic pieces like Goodbye Sky Harbor. They even have a few songs where they have their punk roots sorta showing. They never commit to any genre for any crowd though. I think they are perfect alt rock because of that. Each album they release is sincere and special. I know Invented was a bit slower and did not hit home as much as some may of hoped but I loved it and still think each album embodies a mood or a feeling.