There was a move to oust him when the Deflategate thing happened, because he is rightly considered to be Robert Kraft’s puppet. Goodell was forced to go after the Patriots on that. There was also a move to oust him with the Ray Rice thing.
his job is to deflect bad publicity from the owners. they like that he has to comment on bad things and get the blame
It is why he is paid $30M/year.