If the larger issue is that it hurts the image of the league? That ship, my friend, has long since sailed.
The NBA had an even worse image than the NFL does now. I know you don't follow that league but believe me any fans like me that have followed the NBA can back me up on that. They fixed it and are more popular than ever. And they have grown their popularity globally way more than the NFL has. The NFL can do that too. It is, IMO, right now a matter of willingness on the party of the leadership of the NFLPA and the NFL. Both of which are the worst, maybe of all time in pro sports in the USA.
There are a few issues with this type of stuff. And Goodell has proven to us he just wants to have things "go away" rather than facing them unless there is very heavy media pressure driven by fan reaction to things like domestic abuse and other serious crimes, dirty play, terrible refs, poorly defined rules that help drive the refs bad performances etc.
IMO he does almost as much to hurt the NFL as he does to help it. The Ray Rice video exposed him and his weak leadership ability totally and completely. He saw the tape, and he didn't do anything to alter the suspension. The media got the tape and showed it to the world and then he had to respond. And acting shocked in retrospect was fucked up. If he would have had the balls to address it by saying "we have seen the video from the elevator and outside the elevator and have decided to change the penalty to an indefinite suspension" he would have been in front of this and lauded for it. But he opted for status quo and wasn't smart enough to understand that he had a copy of the tape, which means the ORIGINAL still existed and that shit ALWAYS comes to light.
He handled Deflategate like an idiot, regardless of which side you were on with that fiasco. Same with Spygate, the refs strike, the Miami shitstorm with Incognito, Bountygate, Roethlisbergers sexual assault, AP beating the crap out of his 4 year old son, the concussion thing from start to finish. The list is long.
Every single one of the reasons people are getting worn out by the NFL are fixable. He doesn't have the sack for it. And while he gets a lot of blame for things he shouldn't get blamed for the NFL's image is mostly on him. He's afraid to rip of the band-aid. Stern wasn't. And the NBA is better off now because of it.