Southgate worked and worked set-pieces because he was looking to maximize his strengths; big, tall, strong players who could dominate the box. He knew he was going into a tournament without a playmaker/passer. He obviously weighed up taking Shelvey or even Gobbrick, and realized (correctly IMO) the neither would last 90 minutes against certain opposition, and neither had the discipline to be equally good defensively/without the ball. So, given that Southgate knew he was going into the tournament without a certain type of player, he made the very smart call to maximize every other asset available and looks to have spent a lot of time on set-pieces.
I think personally it would be foolish to adopt his work for the Prem. I am happy that out of his work we get Trippier to offer some variety off Christian.