I don't think it is valid to call one musician the "greatest jazz musician of all time" as different musicians have been great in their own genres. In terms of big band composers/arrangers the top person must be the incomparable Duke Ellington. And in view of the fact that in his role as composer/arranger he was a great creative influence on many other players and composers/arrangers the Duke might be considered the greatest.
If we are talking about who maybe popularised jazz the most then the equally incomparable Louis Armstrong must be up there too. And he contributed not only to the popularisation of jazz but also had a definitive impact on the way jazz is played, so he is also up there.
But jazz is really so diverse that one could argue about this forever without ever getting a definitive answer.
How could one not consider Lester Young, Thelonius Monk, Bud Powell, Charlie Parker, Charles Mingus, John Coltrane, Miles Davis, Gil Evans, and so many others? They all have made huge contributions to the music.
So it's an interesting question, but one which is really impossible to give a definitive answer to.
If I was in a forced choice situation I guess I would ultimately give my vote to the Duke, but with the qualification that even he did not stand alone.