Seems like your place of employment have a bunch of cultural and work process issues to sort out, to be honest.
The diary entries are supposed to replace other forms of communication - not be an addition.
My place of work strive for autonomous teams within specific business domains. You describe yourself as kind of a bottleneck, as things are expected from you in various projects, via email no less.
We’re facing completely different work environments, and as such you see a daily or weekly log as an additional burden. I see it as replacing tones of emails and meetings.
Again - it’s not required here, but as people have noticed the use and asynchronous discussions arising from these log entries, it’s taken a hold. I do them myself as a manager, as my team deserves to know what I’m up to.