This guy is like literally the same size as Dermott: 5'11", 195-200 lbs. Carrick is actually more physical than Dermott as well, so he should even get the edge.
The problem with Carrick is that he did not do the small things well enough. Decent but not amazing at ES. If he knew how to PK, he'd probably stick around or even be in the top 6. However defensemen, especially bottom pairing defensemen, who do not know how to do special teams are limited in their effectiveness. Just like on the other way, being a strong special teamer gives you a lot more rope, much like it does for Gardiner, Hainsey and Polak getting the ice time they did.
Ozhiganov knows how to PK. Dermott knows how to PK and should be starting to do it more in the NHL (they'll probably rotate him, Oz, Rielly, Zaitsev and Hainsey). Polak knew how to PK. Even Holl and Marincin know how to PK, and Marincin is very good at it. Carrick did not, and now look who is on the outside looking in?