You're kind of asking the wrong question. Jazz is complicated now, but it hasn't always been. You're looking at really modern jazz with all it's harmonic complexity and assuming it's always been that way. Jazz is an offshoot of blues, which come from African-American spirituals and work chants, which were very simple, but basic on the African music they brought with them.

You can even listen to the progression.

Work Chants: https://www.youtube.com/watch?v=4G5KtQynWvc https://www.youtube.com/watch?v=wFSlw8LlIw0 Spirituals: https://www.youtube.com/watch?v=7oFcFzJT7Tw https://youtu.be/8zeshN_ummU?t=6m50s Early blues: https://www.youtube.com/watch?v=0mAQ8-uGOuY&list=PLD64CF00BE099BCFC Early jazz: https://www.youtube.com/watch?v=LqEIEDEBnfg

The jazziness comes from the Pentatonic nature of blues (and its predecessors), and the use of 7 chords, and other unusual chords. (I'm going to use technical terms for the music theory behind it, but if you don't understand any of them, let me know and I can explain them)

Traditional African music has a different composition than western music. Western music puts the melody at the top, and uses the major and minor scales for melody. Whereas African music relies more on a melody in the middle, and harmonies above and below, primarily based on the pentatonic scale. African music also uses a lot of 7s and 9s (the seventh and ninth note of the scale) which is kind of the cornerstone of jazz. To Western ears it sounds cool and jazzy, because Western Classical music doesn't use it much, but it's a thousand years old in Africa.

As African American music progressed, you would see next to nothing in terms of music education. Blues musicians in particular, both then and now would pride themselves on a total lack of formal music education, inability to read printed music, and no knowledge of music theory. Even today it's common to find most Blues musicians with no formal music education.

As for the complexity of Jazz, it certainly didn't start that way. Early jazz was quite primitive in its form, and you saw Gypsy Jazz in the 20s: https://www.youtube.com/watch?v=S-Fq9s6hmQc

That grew into Big Band: https://www.youtube.com/watch?v=aE8eXcAvS24

And you'd see people like Charlie Parker who took influences from Big Bad, and saw mainstream music picking it up, so he invented bop to make it harder to rip off (consequently making it less accessible and less popular): https://www.youtube.com/watch?v=Zl5P0cfiR2M

In Charlie Parker's band was a young musician by the name of Miles Davis, who took Parker's bebop and added more complexity and innovation: https://www.youtube.com/watch?v=39jqM5p3SAw

Davis made his own band, and continued to innovate and change the style of bebop. And in Davis' band joined a young musician by the name of John Coltrane: https://www.youtube.com/watch?v=kqI5BHaDgj4

Coltrane took the form even further, doing more experimental jazz and fusion jazz, and free jazz, into the 70s: https://www.youtube.com/watch?v=tgrQhBTDfhk

Now, how did all this happen? Well, at the beginning, there was nothing in terms of an establishment in jazz. No school of thought, or group of people dictating where things should go, or what was acceptable. It was an entirely innovative movement, that was totally outside the Western classical music establishment, was largely underground, and sprung up at the perfect time. In the 20s you saw a TON of clubs pop up, at the same time recording technology, radio, and records were becoming accessible. People could go to one of a dozen clubs in town and hear jazz, and the music would be different every day, because it was a style that was fundamentally improvisational, and constantly innovating by its nature. People were changing the style every day, and you had entirely different styles evolving simultaneously across the country, and into Europe and beyond.

Jazz innovated at a speed that was unprecented. Likely because

a) there was no formal school or style, no accepted practice or technique b) it prized innovation over rigid adherence to dogma c) mass communication allowed transmittal of new works instantanously d) it was cheap to attend, and you had thousands of musicians working on it, and could see new music every day

Throughout this, in order to innovate, a lot of it got way more complex, but not all of it did. Rock grew up from blues and early jazz/big band, and made an entire genre that is far less complex, but way more popular.

But also as it grew, it started to form its own genres and schools, and more formal technique, and more rigidity to the form, which is arguably why it lost a lot of popularity. There's a great book about this called The Death of Jazz that talks about the death of Coltrane, and the rise of backwards-looking musicians like Branford Marsalis caused the decrease in Jazz's popularity. Not sure if I agree with that, but it's an interesting supposition.