Most times I see middle managers meeting (and when I participated when I was one) were about "X is happening, the problem is not (entirely) on my area, let's find where it is so we can fix it".
In my experience, managers have no problem looking busy. They can do that without thinking or conscious effort just by letting the system work the way it wants to. What takes conscious effort is doing anything else.
I'd say most middle manager meetings are for salary justification. They want to look busy.
I guess maybe one or two meetings per week may be classified as 'problem discovery'. The rest is just to make them appear busy and visible.
Agreed with the high management and IC points.