Should a child know what calendars are for? It seems like that could be a useful tool for them to have in their toolkit.

At least for my nieces and nephews, they have as much access to their scholastic portal as their parents. So yes, such calendars are absolutely useful tools. A good thing for parents and children to look at together.

And much like their calendars, we do not ourselves set every event that appears on our calendars.

Well I specifically can tell you every meeting and assigned task, but that's because the meetings are at standard hours and I work on larger open ended projects.

I was also absolutely terrible at remembering what's for homework and when the school exams are... so I learned to write it all down in a notebook so I didn't miss anything. No fancy parent control required. That was basically standard practice ingrained from first grade onwards.