Except last year, where he wasn't behind that many, we literally had McKegg as an NHL center, they still refused to try him then. They even went out and traded for Josh Jooris.
I don't think Billy G really likes Blueger or someone really doesn't. He's having a fantastic season where things are aligning for him in his game and even when this team had injuries, they refused to even try him as a winger - Which of the guys you mentioned in Sheahan, Grant, Cullen, and Dea...they all have played LW/RW and C this season, so being versatile is something that is also hugely important.
But why bother trying him at all, right?