I don't think Norv Turner has a history of favoring the shotgun above all other formations. This is more of a new wrinkle across the NFL the past hmm 3 to 5 years where teams are using more pistol and shotgun formations and spreading the field out with multiple receivers. To complete that package you want a RB that is good at running out of the shotgun, which a lot of the younger RB coming into the league these past few years have a lot of experience with it.
The pistol is designed to help the RB not give up a side where he is lining up. Because without TE or a FB it becomes easier for the defense to overfit the 5 linemen. The direction of the play becomes more predictable out of the shotgun where the types of runs are somewhat limited.
I think Turner is running the offense the way that it is because this is what best suits Teddy. I don't think it suits Peterson very well. Peterson would like to run out of the I formation so he can press the hole and then bounce it at the last minute. It is harder for him to feel the flow of the play and to set defenders up running a draw or inside zone. The draw generally works best when the defense isn't expecting a run. Defenses do not really every expect the Vikings not to run with Peterson.
There was
an article written about this by Ben Goessling back in November. He explains how the Vikings built their offense around Bridgewater not Adrian Peterson.
Not so many years ago I think the offense was completely built around Peterson. For example Phil Loadholt who the Vikings were willing to sacrifice some pass protection ability because he is such a good run blocker (something Clemmons is not right now). In some ways Percy Harvin and Patterson are meant to be support players for Peterson and the running game.
When Peterson almost broke Dickersons record in 2012. I recall a substantial portion of that yardage happened on runs with a FB on the field. In this case Jerome Felton.
Peterson has said previous to this that he preferred running out of a single back set. That he didn't like to be patient and wait for the FB to make his block before clearing to the next level. After having such success running behind Felton, I don't think he felt that way anymore. He has mentioned many times that being patient and waiting for his blocks is a struggle for him to do at times.
So you have two different offenses in a sense here. The offense that has developed around Bridgewater in Petersons absence, and the remnants of what they planned to do with Peterson before adjusting to not having him. They are still learning how to best use Peterson, which is a bit ironic considering Norvs history.
My main gripe is that if they are going to utilize a FB, which they have had Zach Line on the field for 19% of the plays thus far over 4 games, then they should have kept Jerome Felton, who is a much better lead blocker than Zach Line is.
The coaches have the bye week to figure this out. I don't think you throw out plays that are good for Teddy just to accommodate Peterson. I do think they are still trying to find the right balance of plays and play synergy now that they have Peterson again.