I wonder how many direct reports these managers have. Does anyone have insight? I believe 1on1 is good from my experience in companies where there is a lot of change and a lot going on the #1 feedback I get is people want more information, more 1on1, more team time. With roughly 40 direct reports 1on1 is nearly impossible with the other demands.
At one time I had multiple teams with 16 direct reports - at that point it was very hard to have a weekly cadence for 1:1's with everyone, as that would've been 8 hours a week. My solution to this was to start with bi-weekly 1:1's, having 8 people scheduled one week, the other 8 the following week. Then each week I had office hours scheduled - this was time dedicated to the team to be able to book my time and was not allowed to be booked for any other meetings - this way people who wanted to meet on an off week could. The second step was determine who could (and wanted) to step up in to management roles - ultimately, this lead to promoting two managers under me, and moving their direct reports to being a monthly skip level 1:1, reducing my overall bi-weekly 1:1's across my part of the org.
Honestly, I think 40 direct reports is borderline insane. You can't effectively support that many people (as you note yourself). Speaking as the author of two of these READMEs, at Netflix I had at peak around 12 direct reports (one was a manager with his own reports) and at Slack I have 3 (all of whom manage their own teams).