While Parker stated how fantastic schooling was, he had no formal training beyond high school. That was due to the "economic reality" of most jazz musicians.
"Study is absolutely necessary"; whether formal or informal, initially, all great jazz musicians put in most of their waking hours toward mastering their instruments. During Birds time, some highly acclaimed institutions scoffed at "jazz", just ask Miles, who went in the front door and out the back of Juilliard. (Founded in 1905, The Juilliard School is a world leader in performing arts education.)
Whether one goes to a formal school or is "self taught", intensity of study and practice is necessary. I wrote about a musician who "never" practiced; that's because he was performing "improvisational hard bop jazz" three times a week. (If he had not been performing constantly, practice would have been essential)
He was 36 and looked 26 (I was 26); I bet you can guess his name. Before I met him, I'm sure he had spent most of his life practicing because he "never" looked at the organ keys; quite often his eyes were closed.
At that time there was a club devoted to "Improvisational hard bop" (no standards). That's what the audience that patronized that club demanded, and that's what he gave them.
In my mind, there is no greater musician than one who can constantly create on the spot; "The improvisational jazz musician". Next would be "The pit musician". While the pit musician went through many years of formal training, and can play anything that can be put on a sheet of music paper, he can not spontaneously create all night long.
I suppose comparing the two is like comparing "raw talent" to intense formal training and practice. I've compared the two, live in real time, and they are a sight to hear and behold.
If I was left on an island with only one record to play, I would choose "Bird With Strings".