Your model assumes the CEO and all others on the path are full time people managers. In reality, the upper layers of management have many other roles, from customer engagements to political lobbying to CSR to strategy etc. They can manage nowhere near 22 direct reports.
Additionally, geographic distribution is important. You can't have one manager in the USA managing 7 direct reports from Germany, 7 from India, and 8 from China. So, you need 1 site leader for each of these, that the 6-7 middle managers report to. These all add up very quickly to take the theoretical 2-3 minimum required layers to 6-8 layers in practice, without requiring any of those along the way to be micromanagers.
Additionally, geographic distribution is important. You can't have one manager in the USA managing 7 direct reports from Germany, 7 from India, and 8 from China. So, you need 1 site leader for each of these, that the 6-7 middle managers report to. These all add up very quickly to take the theoretical 2-3 minimum required layers to 6-8 layers in practice, without requiring any of those along the way to be micromanagers.