Not necessarily. There is a big log jam at forward, especially on the wings. Do you think Laich, Greening, Leipsic, Kapanen, Michalek, Rychel, etc. shouldn't also be in the lineup right now? They are all guys who can play well in the NHL right now. But there are no spots available, and up until the Leafs traded Holland (the one person you can say Babcock didn't like), the Leafs had negative spots available for someone like Leivo.
If Babcock put Leivo in, who would he replace? JVR, Komarov and Martin aren't happening. Nylander, Hyman and Marner not also. So it's either Brown or Soshnikov. Would you rather have Leivo in as the 13th forward, or one of those two as the 13th forward/in the AHL. Most likely, we'd be having the same conversation as the one we are having right now, except sub in Leivo's name for Brown or Soshnikov. That's the decision Babcock is facing right now. Leivo is coming off of injury and it looked like it was still affecting him in the AHL, so that's probably the deciding factor for him right now.
Leivo will get into the lineup soon enough, it's just a matter of injuries, illness or maybe a forward needing a game off for him to sub in there.