Of course, I agree its a tough job. I have no problem with some sort of independent process. But abdicating it completely as suggested above is not a solution.
Meaninglessly flailing around because you have to do "something" doesn't help anyone - in fact it generally makes things worse.
Domestic violence is a huge complicated issue - and we need to deal with it at a societal level through education, providing shelter and resources to victims, etc. The NFL flailing around and suspending players seemingly randomly is not helping prevent domestic violence in any sort of way.
Ray Rice had already been arrested, charged, indicted, (then married the woman), rejected a plea deal, and then entered a pretrial intervention program for first time offenders before he even had his first hearing with Goodell. Do you think that the shitshow that happened when the NFL tried to be involved (and botched pretty much every aspect) made Janay Rice (or any other woman) safer? I don't. All that shitshow did is make the NFL look incompetent.
The NFL did a 10 month investigation into Josh Brown (so they say) - and said that with the fact that the victim recanted, there were no charges filed, a general lack of evidence, and the DA involved saying there was no case they couldn't justify more than a short suspension. And it blew up in their face. There's 2 possibilities here - he did it, and they're soft on domestic violence, or he didn't, and they're suspending players for evidence-less allegations. Either one makes them look bad.
Now, maybe the perception that NFL players are wifebeating assholes is helping to offset the fact that the NFL is destroying it's employee's brains (they're villains, they deserve it) - but I don't think that's enough to offset the fact that it's making people not want to watch.
Eagles LB Nigel Bradham has been arrested twice this year (and once a couple years ago for weed) - once in July for assaulting someone in the lobby of a hotel, and a couple weeks ago for carrying a loaded gun onto a plane at Miami International. I think it's undeniable that his crimes have been significantly less damaging to the NFL than Josh Brown's - and that's largely because they've (to this point) let the justice system handle it - and not called attention to it.