The question is about Garrett as the Head Coach, not as the OC. I've always said that he was the right HC, but should delegate the OC job.
The part of the HC's job that relates to building the right team mentality takes time. In my estimation the rule of thumb would be about a 2 to 3 year delay to see results in this area. Garrett had to inherit a locker room that was a complete disaster. Remember when Parcells told the players not to "eat the cheese" in regards to not getting an inflated ego? Wade basically had semi-trucks of cheese force fed to the players when he was the HC. That team ended up with leaders like Jay Ratliff. They were a bunch of entitled underachievers. The only guys that didn't fall into that were Romo and Witten who were tight with Garrett. Even as OC Garrett stood up to TO when Wade wouldn't or couldn't.
Wade inherited the opposite from Parcells. That team was well disciplined and went 13-3 in his first season but steadily declined as the lack of discipline caused the players to develop an overwhelming sense of entitlement and eventually they just quit on Wade.
Garrett took over for Wade at mid-season and managed to get a 1-7 team to go 5-3 in the 2nd half of that season. After that the team mentality had to be purged and that is a slower process when a bunch of players have contracts that prevent them from being cut immediately.
It might have been 3 straight seasons of 8-8, but there was progress in 2013 despite the record. They had 3 losses by only 1 point that season, another loss by 2 points and another loss by 3 points.
It's fairly obvious that the current locker room mentality is what you want and Garrett has done an excellent job of building up that winning type mentality. The only player that might have any of that Jay Ratliff type of over-entitlement would be Rolando McClain and he is basically a loner on the team, not a leader like Ratliff or TO. McClain only got a veteran's minimum deal plus incentives which also limits his impact on the team.
The front office might have under-cut Garrett a little this season. Garrett really wanted to keep Murray but the FO didn't. Garrett valued his leadership and no nonsense approach to the game. Keeping the right locker room mentality is a high priority for Garrett but the FO saw the probability of decline as high for Murray based on the history of RBs at that age and when coming off seasons with super high numbers of carries. Hopefully, the FO made the right decision.
Building the character of the team is by far the number one job of the Head Coach. Many coaches can do the X and O stuff. Since off-loading the OC duties, Garrett has not had any in-game issues which people criticized him for in his early years as HC. Jimmy Johnson said from the beginning that he thought Garrett would become a very good HC, but as a young coach that he should not be both the OC and HC.