The thing is, highly skilled employees are only effective if they work in a coordinated manner towards a common goal, and the people in charge of coordinating the teams are... Managers.

To put it differently, in a 6-man team each employee is responsible and held accountable for around 1/6th of the productivity, but the team manager is responsible and accountable for 100% of the effort.

Hence managers earning higher salaries.

The manager is not responsible for doing any work, only meta work. The metric of work output measures mgmt value input indirectly. You need to look at their actual interaction and analyse the meta work they do directly to get a true account of the value a manager provides.