While I do agree with your overall point, sample size is way too small to look at WOWY stats, not that they're without their own problems in general.
Also, I disagree that he likes to be the "third man back." Well, firstly, the Flyers love to operate with a center breakout so the d try to get it to Coots who hits his wingers out of the zone for those quick breakouts -- which he is immaculate at generating and one of the best on the team....minus his turnovers the last couple games haha. So that's in the system, not Coots being extra "defensive" or anything. But he activates plenty himself to skate the puck through the NZ. I do think you're selling him a tad short with his own work on the rush. Starting in the latter half of 14-15, he's significantly improved his confidence in skating pucks in each season. But, yeah, his ability to get in position for a pass from the d or retrieve the puck himself and then make the successful pass out is absolutely vital to their transition success. To say nothing of him being a ridiculous forechecker and boards player to keep possession once they get it in.