Management is knowing of to make people work together toward a common goal.
1. A managerial role is not _easy_ to hire for if you're looking for someone who has (for a start) correct skills & experience to manage a team (of engineers only, or of various backgrounds).
One of their roles is to help his team focus on what they want to/can do for everyone to succeed. That implies a lot of ingesting, structuring information and communicate it in all directions, all of the time. You need practice, and skills, to handle that without becoming completely numb.
2. Technical skills aren't everything. Far from that. When hiring, it's among the last items on my checklist. You want people to be motivated for the job, to be capable and willing to work in a team, to be willing to learn and spread what they learnt. What they know and can bring in total derives from that.
3. You get 1 manager for several members of a team. And a manager also coordinates with other managers & team members. Budget-wise, you can take and compare the manager compensation with any one team member's compensation but that does not make much sense.
4. Companies success being the result of (mostly) the technical excellence of their teams is the worst toxic professional myth I've encountered; it took me 5 years to see it and 10 more to accept it.
Purpose/strategy (know what you want) + design (know how to get there) + logistics (know who/what to ask for it) trumps most of the rest.
The bonus is if you also have the technical skills to do it but that's not a requirement.
Being an engineer is great, I love it. But it's far from being THE ultimate valuable role in a company.