I would expect that CAPsMan is dividing the channels in such a way that there is a minimum overlap. Or or are my expectations incorrect?
No, CAPsMAN does no coordination of channels between APs. The auto-frequency function in the AP takes only that AP into account, and the way it works is that it does a wireless scan and counts the quantity of detected APs on each frequency and uses the frequency that has the fewest APs on it, ignoring the signal strength. So if every frequency has 2 or 3 APs each of which are far away and so the signal is -90 or worse, and then one frequency has only one AP and that AP has a signal of -50, the auto function will jump on the same frequency that has the AP with the -50 signal. Therefore, in those cases, the auto function can easily pick the frequency with the highest amount of interference instead of picking the frequency with the least interference. In reality, I see this happens quite frequently, where all of the CAPs like to herd together onto the same frequency and interfere with one another, and so it becomes quite important to hard set the frequencies to prevent this.