Everyone multitasks. You switch from email to a project schedule to a requirements document within minutes, or seconds. You (and everyone else) brings their laptop to a meeting so they can crank out emails. Everyone multitasks, but most people aren’t good at it. Research from the University of Utah (here) shows that less than 3% of the population can multitask with no decline in performance.
To a degree, PMs know that people are bad at multitasking. We would rather have one person 100% of the time on our project instead of five people 20% of the time (assuming equal talents). Then we know what they are working on at all times.
There are certain tasks that don’t suffer if you do them poorly. Many of the tasks that PMs do, such as tracking task completion and issue tracking, don’t require a high level of performance. But you should be worried about your job if all you do is menial tasks that can be easily done while multitasking. Some of the problems that need solving are hard and require full attention. If you aren’t working on the hard problems, then you may not providing value to your organization. You are paid a lot and you should be spending a significant percentage of your time solving hard problems.
It’s clear that people should complete one task at a time. You and your team.