I think it misses the point of DevOps. My reading of DevOps is not that developers do operations. It is that operations applies development style processes to their job and works closely if not within the development organizations to make sure the application is designed for operational ease from the beginning. A DevOps specialists will be operations focused with a high degree of skill in the scripting to automate deployment and configuration. They will use version control in order to version the deployment and configurations with the application. That way when a version of the application is deployed to a development environment, testing, or production the exact same software not just for the application but the deployment and configuration is used. The goal is so that when things go wrong it is not due to some untraceable human error, but a fixable automation error.
And, DevOps doesn't mean operations goes away. I think it let's operations focus on delivering a stable platform for applications. i.e. servers, disks, networks, OS, and perhaps the software repository that DevOps can use to configure the platform and deploy applications. In infrastructure as a service cloud situations, servers, disks, networks, and OS become a DevOps responsibility, also.
As far as a DevOps role, I think this falls into the same mistake I get into in my company when trying to explain the concept of Agile team members and feature teams. Just because everyone on an Agile team should be able to take on any task to deliver the software doesn't mean you don't have specialists in Dev, Test, and Analysis. It also doesn't mean that you assign tasks stupidly to those least capable. Most of the time people will be working in their specialty, but they have secondary skills that allow them to take on other types of tasks when over flow occurs in those tasks. A DevOps specialist is focused on the deployment and configuration process and they primarily get that kind of work, but can help with other types of tasks when necessary. Similarly, just because teams are capable of working on any part of the application doesn't mean they don't specialize or that you assign work to teams outside their specialty willy nilly. But, if it looks like there is a long term need for another team in some application area, it is possible to have a team move to that specialty and ramp up their capability there with the help of the existing specialists. It might make sense to have a DevOps specialized team with multiple specialties (SA, DBA, scripting, support) represented in that team, but with flexibility to handle work in other areas, but perhaps at a lower capability that a team specialized in that area.