Musically, "Hey Jude" isn't complicated. There's no introduction; for the first eight bars, we hear only piano and voice. New instruments are added slowly, even methodically: the rhythm guitar and tambourine in the ninth bar, background vocals in the 13th, the drums in the 16th.
The harmonies become a more significant presence as the song progresses, but they still remain just harmonies. They add nuance but not a great deal of dimension to the song.
It was clearly McCartney's intention to sustain focus on the piano and the vocals from the song's beginning. Lead guitarist George Harrison wanted to add a guitar riff at the end of each line, but McCartney said no. He allowed Harrison only the simplest of bridges; the melodic burden was left entirely to his own vocals.
At roughly the midpoint, the song segues from its original verse-verse-refrain structure to four minutes of a "na na na na" bit. The lengthy non-fading fadeout was largely unprecedented and somewhat risky for a song intended to be a single. Producer George Martin warned that no radio station would play a single that was seven minutes long. "They will if it's us," Lennon replied. (Source)
And he was right. The song spent nine weeks at the top of the American charts. Moreover, in many ways this second half was a song within itself. Volume and instruments are added—not reduced—eventually a 36-piece orchestra and an unknown number of additional voices flesh out the sound of perhaps the most epic outro in rock history.