As someone who has lead a devops team, and still has a devops team reporting to me, I have also struggled with the idea of having a team called devops, since it does go against the devops philosophy of devs owning their software in production. However, in our case (and probably many others), our devops team is responsible for creating and maintaining the tools and processes that allow the dev teams to manage their sy…
It's sort of like expecting you can get by with only sales engineers. Having someone good at either job is hard enough, expecting you can staff only those that are just as good at both? Reality is you'll just end up with people deficient in one area or the other.
You might get by with a small core of people that can successfully straddle both roles, as long as you don't expect them to fully handle the needs of both departments, but I suspect hiring only for either department and fostering good communication and encouraging them to work together on projects that help deployment and availability yields better results. Maybe that partnership will grow you some good devops people if you're lucky. Maybe you should resist making a department out of them if that happens.