Hawk's long and winding road to the NBA resulted in his having a game that was truly unique.
First, because of the gambling pseudo scandal, he never really played college basketball at all. He was only on campus at Iowa for a semester and a half, thus he wasn't drilled endlessly in the "fundamentals" and constantly reminded of 9000 reasons why he couldn't do stuff.
Then he went to the Pittsburgh Rens of the ABL, an abortive league which played a season and a half. He was by far the best player in that league, so nobody else told him not to do anything there either.
When the ABL bit the dirt Hawkins went to play four seasons for the Globetrotters, where instead of telling him not to do flashy stuff, they told him to do anything flashy he could think of. This was where he developed his one-handed palming waving the ball style.
Then he joined the ABA where once again
he was probably the best player in the league and no coaches were likely to lecture him
about fundamentals.
Had Hawkins followed a more conventional college-then-NBA path for his career, his style probably would have been more conventional as well.
Also most of his career was played in substandard leagues (with probably substandard medical care) as well as thousands of games on blacktop, plus the overall level of treatment for knee injuries was still in the relative Stone Age, he was already hobbled by major injuries before he arrived in the NBA at age 27.
So essentially, he missed about a decade of a career which might have been something quite like Elgin Baylor's.