I don't think the nhl did "great" under bettman. He was maybe "okay" but not "great".
What the nhl wanted from him at the beginning was a legitmate national US deal with the networks. They got it with fox.
I think the 3 work stoppages under his watch are big blemishes. 1994 was damaging because they had awoken the largest market in America. Sports Illustrated was also pumping the nhl tires while deflating the NBA.
2005 was ridiculous. A full year lost. That just does not happen. Then yet another stoppage in 2013.
There was also short term vision of taking a TV deal on an obscure network such as oln/versus. For a niche league trying to keep up with the nba's growth, they sure did their best to hide their product from the mainstream sources.
That said, yes the league definitely grew under bettman, and they are a much more professional operation than what he took over, but that was inevitable if the league hired anyone with an ounce of competency for the job.