That's arguable. Carrick had numerous subtle attributes, and one that was top percentile in the world, was his two-footedness (ambidexterity), which meant he couldn't be pressed/forced to a 'bad' side and hurried into a-then poor or weak pass. It also meant he could shape towards the ball from any angle and immediately control or relay it without having to think about his actions - Carrick could drag opposing numbers out of position in this manner and render them redundant for a few moments - certainly enough for us to exploit the vacancy - and set us off on our way. He didn't have nimble feet, so could be gotten to in a double-press as he rarely dribbled out of a situation, but in committing more than one man to do that, the opposition also leave huge gaps and a simple pass to the more able Scholes to create chaos would nearly always be on for him.
Carrick's positioning was top percentile, for sure, but the way he could use both feet, as well as progress the ball with them, was absolutely intrinsic to our play. I don't know if it's right to say either attribute was better than the other, more it's right to say he was outstanding in both aspects.
I think the semantics of the term are the issue here. For some, the definition of a DM, is someone who sits at the base of midfield, covers that area specifically and does not go hunting for the ball; others use a much broader stroke of the bush and consider runners/terriers/harassers, or whatever interchangeable term you want to use, as DM's. There has even been a time when the two roles were identified separately as DM and DCM, with DCM meaning someone of the latter category who did run, ball/man hunt and harass all game long.
Some people call the likes of Keane, Vieira, Gattuso, Davids and Essien DM's, where for others, that's crazy talk with, for them, the DM being a strict definition of a midfielder who simply sits for the majority of the game and possibly ventures forward or towards the ball a tiny percentage of the time - the likes of Makelele, Dunga, Deschamps, Mauro Silva and so forth typifying that. I'm using players from past decades because it's easier to define than what we have now where roles are not as set in stone and the way systems are used blurs the lines of what players 'are' quite a bit.
If the issue is semantics, are you saying Kanté is a DM because he is a destroyer? Or are you saying it because you believe he sits and protects and does not vacate his position in pursuit of the ball?
I notice in your terminology, you have 'DM' and 'AM', where is 'CM' if we're to cover all of midfield? Surely that's what Kanté is best described as?