If you think about it, 16 minutes isn't crazy.
Your typical 4th line should play about 10-12 minutes of the game. Glendening was Detroit's top PK guy, so if there were games where Detroit got 3, 4 , 5 penalties, and Glendening is playing the majority of the PK minutes, there will be games he plays those minutes.
Not too mention, most of those where in the 2014-15 season, where after Pavel Datsyuk, the Wings centers were; Riley Sheahan, Joakim Andersson, Stephen Weiss, Darren Helm, and Luke Glendening. The only one who remained healthy all year? Luke Glendening.
Datsyuk only played 63 games, Andersson 68, Weiss 52, Helm 75, and Sheahan 79.
There were times even with Zetterberg was moved over, Glendening had to play top 9, and even top 6 5v5 minutes on-top of the heavy PK minutes he was trusted with.
So yes, for parts of that season, he had to play 16 minutes or more, but it isn't because Babcock overplays him, or he's a "pet", it's because they had no other options.