Not sure this is accurate. When it comes to player punishment, the most appropriate criticism that could be made of Roger is that he didn't do enough in his early years to punish players with DV issues.
Can't remember where I saw it, but there was a list of players with DV cases who basically went unpunished. No suspension at all, in some cases.
Here's a similar list.
Goodell only cares about his authority as much as he has to. He only cares about his authority as much as the owners make him care about it. Prior to Ray Rice, players were given passes left and right. Since Ray Rice, nobody will get a pass. Goodell -
via the owners - does not want to appear as though he is screwing this issue up again. If that means some players are inappropriately punished, then so be it. That's better for the league than appearing as though they aren't doing enough.
Goodell likely only prizes 1 thing, and 1 thing only. His paycheck. He's going to do whatever is necessary to protect that paycheck. That means he is going to do whatever the owners want regardless of whether or not he should.