DevOps itself is a loaded term that means a lot of things to a lot of people. But the need for the terminology highlights an important point: drawing hard lines between development and operations has led to much pain in the history of building and managing software systems. Companies that keep their sysadmins in one building and their programmers in another are having their lunch eaten by companies who realize that close collaboration is necessary, and that team boundaries need to be drawn where they make sense based on the specific problem at hand, not where an HR person's knowledge ends.
The fact that so many questions are being closed on Stack Overflow for being offtopic when they are talking about things that bleed pretty deeply into programming is troubling to me because it indicates an impulse to cram things into a rigid taxonomy that does not fit the direction the software world is moving. A dedicated DevOps site would dilute strong questions and answers on Stack Overflow in favor of servicing such a taxonomy.
Obviously we don't want every software package under the sun to spawn a zillion off-topic Stack Overflow questions, but programming is a messy thing and there should be some nuance to the fat we are attempting to trim lest we start cutting meat as well. Stack Overflow is of course the original and largest, and therefore will necessarily have the messiest edges. We need to wrestle with the messiness and come to reasonable terms that maximize the utility of the resource overall.
My worry is that the people making these decisions are not the ones getting the most use of Stack Overflow, but are the people most drawn to tidiness and organization for its own sake. I'm reminded of the problem that Wikipedia has where the domination of the community by policy lawyers with no actual domain expertise allow bad content through based on a (possibly malicious) contributor's willingness to jump through hoops, where real topic experts through up their hands and give up their efforts to correct obvious falsehoods because, you know, they can be more effective in other areas of their life where their expertise is actually recognized!
In short, I feel very strongly, database storage is cheap, the search feature is effective: DevOps questions should be allowed on Stack Overflow.