I never really saw an issue where he got caught skating with the puck, or where he couldn't skate into the open ice in the middle to receive passes, or couldn't make plays off the rush.
What I saw routinely was him skate into the zone with the puck with time and space to make a play, then hold onto the puck, then hold, then hold, and either try to play off the contact and lose the physical battle, or make a low percentage hope pass, and turn it over.
After skating 100% on both the forecheck and backcheck all shift.
That's why I think his natural athleticism and perhaps conditioning, along with his choice of style, are more of an issue than his actual skating. To play Bednar's system specifically.
It will be less of an issue on a slower team where he can coast more often and read the play, if he actually chooses to do so, because he'll have to have to change his approach to the game to do.