The general preconception about managers: people in expensive suit spending all the time on unproductive meetings, pretending of doing something. They are managers because they failed to learn other job. Managers and engineers have nothing to common.
You believe or not, but the above statement is not true!
The cause for the misconception is that yes, there are bad managers. Just like in any other profession.
The concept (and the reason) of the management as a science is the fact that team and organization can deliver more if they are well managed. A good leader worth lot more then a good worker! Therefore the responsibility and contribution of a manager should be higher.
Because of the higher responsibility and contribution to team performance, the salary is higher. You want to get the best people for the most demanding job. Unfortunately some people go for the money and not for the work.
I am not going to tell you who the good managers are, but I tell you a very interesting observation: in companies where the culture was good, and things went well (in both professional and financial aspects), the distance from management and employees was low.
In such companies the director of engineering was a director with engineering background in the particular subject along with a long proven record of management experience. The director, the mid-level managers and the engineers knew all about daily operations. If a new engineer hired, the managers could explain him what his job was and how to do it. Well, the difference was that engineer had more up-to-date expertise in engineering then the director, who had lot more expertise in management then the engineer.
Those directors always cared about their people, about their knowledge (e.g. never outsourced key roles). Those directors never kept distance from the engineering floor, and never wanted to be VIPs. Those directors had understanding of everything going in their domain (not always in full, but some).
Why this is important?
Because projects in the 21st century are never huge. You will never lead a 1000+ people project organization directly. Instead, you will lead team of 10-20 plus a net of contractors, subcontractors and their subcontractors (2nd and 3rd tier suppliers). The sum of people working on the project could be the same 1000, but directly you lead only a small team.
So you will lead small team in either way.
If you are not capable of leading small teams effectively, because you feel only "huge projects" are the right size for you, then it is time to start a new career!