I'm not so sure your usage of the term "full-stack engineer" is accurate here. I consider myself full-stack, but I don't know half the stuff about Chef that our DevOps guy does and I'm ok with that. To me, a full-stack engineer means that I'm capable of coding both things that make magic happen in the browser and things that make magic happen on the server side of the application. It doesn't mean I'm a jack of all trades.
That said, I don't think that the increased prevalence of DevOps is bad. And I don't think it means "everyone is doing everything" either. It's a new role that is borrowing elements from both development and operations. Not one person doing both roles.