Most folks (certainly not all!) at the Director level and higher by definition spend their entire day talking about work other people are doing rather than doing it themselves. It's the nature of the beast, especially if you operate with a manager only having one or two small (3-6) person teams to manage. You can get a flatter org chart where managers have 15 or 20 direct reports, which makes it impossible for the manager to both be a good manager and GSD, or you can have managers who still GSD but you have so many of them you start to add layers so that the C-level can still do what they need to (get investment, or drive revenue, or strategic partnerships or whatever depending on your scale/stage).

It's depressingly easy to end up in a situation where the line employees are overworked and underpaid, the first level managers are stressed out trying to really manage well their half-dozen direct reports while still producing work themselves, and the Directors and VPs end up passing reports back and forth all day, every day.

Studying span of control, managerial time allocation, and corporate promotion criteria becomes more interesting the further I get into my career. They literally define (or change) companies.