Docker runs fine with multiple processes in a container.

I think that, while most people realize this, it's important to highlight this fact again. Generally, the examples you see are "look, we can run this would-be-backgrounded-elsewhere daemon in the foreground in its own container!", when IMO this sets the bar a bit low for how people initially approach Docker. Containers have simplified my life significantly, and (again, IMO) their real power becomes evident when you treat them as logical units vs individual components.