With three prominent interviews in less than a week, this looks like a coordinated campaign to 'rehabilitate' his image, which (despite what his defenders here say) suggests that he knows its needed.
If that is the case, then he has clearly fallen short of his goal. His 'transgressions' against the likes of Marner and Franzen were not so great that they could not be rectified by an unconditional apology. He doesn't need to do charity work or any penance of any sort; he literally just needed to say "sorry" without all the other "well, actually guys, I'm a really good person" stuff. That is PR101: say sorry, kill the story, move on with your career.
The fact that he couldn't do that, IMO, speaks volumes about where his head is still at. It also would make me very wary of hiring him if I were a GM. Because that inability to just check one's ego, to understand that one does not always makes the right decisions, that was the problem here. And it was an on-ice problem. The Marner story is valuable as part of the larger picture but from strictly a hockey POV, Babcock's inability to reign in his ego hurt the team. He refused to change a system that was clearly ineffective, even going into his final season, when he knew his job was on the line. He refused to take in opinions on a player's abilities other than those which aligned with his own. He not only overplayed players that he liked, which every coach does, but he did so to a comical extent.
On top of all that, there was the undercutting of his own GM. What other coach took pot shots at his GM in public? Sure, sometimes you'll hear "We need more" or some vague catchphrase indicating frustration, but no where near the extent. If you are a GM for a team, why would you want this guy to work for you? So he can tell the media how much your trade for a top 4D sucks?