It's clear Cooper's system changed, and it's also clear Yzerman has pushed for this "safer" approach, probably starting around the beginning of 2016.
http://www.foxsports.com/florida/video/918833219639
He's waaaay more concerned about scoring chances against then he is our own scoring chances from that video
It's pretty obvious that he didn't like Cooper's run and gun. He's given Cooper the chance to adapt to his vision, which isn't a style that made Cooper successful. He's had some success with this like in 2016. We won games, but we looked worse. We didn't have the puck as much. Wasn't as fun to watch.
So if Cooper does go, Yzerman's comments make me believe he's not interested in a Bruce Boudreau type. I also believe Drouin and Cooper could have gone on and had a good working relationship. Drouin did say he envisioned staying here, but as evident from the trade, Drouin wasn't part of Yzerman's style.
TLDR; Cooper is being pushed to change from what made him successful.
That could actually be true.