My personal opinion is that no one HAS to go through the experiences you list. While incredibly valuable, these experiences will certainly affect a person's individualism, which in many ways is a key component to free improvisation.
Couldn't it be said that knowledge of jazz history might impact a musician's every decision/reaction, thus decreasing the distance that player has from preconception, tradition, and a true free nature?
An extreme example: a savant may pick up a tenor saxophone, having never seen the instrument, or knowingly heard it's accepted uses, and approach it's use in a very different way.
This person may have an incredibly broad and deep emotional spectrum, and an incredibly sensitive ability to interact with others, having never done so in a musical setting.
It is up to the critics to describe the individual's merit.
Maybe that wasn't the actual direction of this topic, but...