> “We found that on days when managers reported high email demands, they report lower perceived work progress as a result, and in turn engage in fewer effective leader behaviors,” says Johnson.

It seems this is largely a disparity in expectations of work. The managers self-reported feeling like they got less done when replying to more emails. But isn't supporting their team and being able to rapidly answer questions often part of a manager's job? And if not, perhaps they are in the wrong role.

I would be more interested in measuring overall team productivity, not just the manager's self-reported version. I think you might find that the high-email-throughput teams do get more done with that extra emailing, even if the manager feels like they have been less productive.