Managing containers with Docker tools
You've seen that you can use existing Windows tools to administer containers, but what you can do with these tools doesn't always apply in the Docker world. A container will run a single web application, so the hierarchy navigation of IIS Manager isn't really helpful. Checking event logs in Server Manager can be useful, but it is much more useful to relay entries to the console so they can be surfaced from the Docker API.
Images also need to be explicitly set up to enable access to remote management tools, exposing ports, adding users, and running additional Windows services. All this adds to the attack surface of your running container. You should look at these existing tools as useful in debugging in development and test environments, but they're not really suitable for production.
The Docker platform provides a consistent API for any type of application running in a container, and that's an opportunity for a new type of admin interface. For the rest...