I don't think he is the 3rd wheel. Quite often when they get established in zone, it's Nuge who gets the puck, while McDrai try and get lost in the shuffle.
It's his job to read the PK, and try and move guys out of position in order free up space for McDavid and Drai to attack once the puck gets to them (after 1 or 2 quick passes). Very much the QB trying to read coverage and hit his receivers in space.
Imo that's the secret formula to the Oilers PP: once they're established in the zone (becasue McDavid is zone entry god), McDrai don't really get the puck until breakdowns are already occuring. They still draw a s**t ton of attention, and that's what gives Nuge (plus Hyman and Barrie) all the open ice to pick the PK apart and create those breakdowns.
As weird as it sounds, Drai is generally the 3rd wheel on the PP, and the easiest member of the big 3 to replace. Mainly because he handles the puck the least, plus McDavid can shift to the RW halfwall while Kane or Yams can take over as bumper.