Many players lose sight of the fact that there actually is little that they can do to hide their individuality. That point comes when the player needs to make a more personal statement and attempts to communicate this to an audience. Then one should abandon all attempts at emulation and begin to develop an individual sound and vocabulary. I have found that there comes a time when it is important to actually tune out or move on from major influences. This does not have to preclude being inspired by others because it is distinctly possible to appreciate another's artistry and instrumental accomplishments and even be influenced without directly emulating their style.
Style is really a byproduct of the artistic prerogative.
It is the surface characteristic of a player. If you emulate a style, then you are only emulating the surface of another. Some are such original thinkers that they are able to invent a new style and vocabulary. Louis Armstrong, Roy Eldridge, Thelonious Monk, Charlie Parker, Lester Young, Jimmy Blanton, Dizzy Gillespie, Miles Davis, Lee Konitz, John Coltrane, Ornette Coleman, Eric Dolphy, Elvin Jones, Donald Bailey, Eddie Harris, Elmo Hope and Herbie Nichols are a few that come immediately to mind. Often, this is done by consolidating, sharing and extending the vocabulary of what came before.