I guess, a very important skill is to say no. It's ok to be unavailable to finish a task.
A meeting without an agenda, from my experience, lacks focus and consequently often results. Sometimes asynchronous communication is enough... Personally, i try to concentrate meetings to specific days of the week, so that i have two, three days a week without major interruptions.

Regarding operations, i like to cite: "unplanned work is death to all other types of work, such as planned, or projects"
We do have an operation center, which routes events, incidents, information coming from all types of ingress(events, email, calls, incident tickets) to specific support groups.
Support groups, as does mine, have a so called "dispatcher" role. Someone's main task for the week is to acknowledge incoming events, and to try to solve most (small) tasks themselves - to keep everyone's back free; to concentrate unplanned work of the whole group.