Having been in the industry for 15 years, and having been both a hard developer and an engineering manager, my two cents:
1- managing a team of engineers WELL is really hard, and requires a broad range of skills. Granted, there are a lot of bad managers out there, particularly in engineering.
2- managers aren't getting paid for their productivity, or even their time. They are getting paid for judgment and accountability. They are accountable for the output of a whole team, and they can only indirectly influence productivity of each engineer.
3- I can say this because I'm an engineer- lots of engineers (in fact, many of the best ones) are immature and stubborn. That hurts teams, hurts feelings, and inhibits productivity. Don't underestimate the difficulty in keeping things running smoothly on interpersonal issues.
To the above points, I was a manager for 4 years. My team members said I did a good job. Yet, after sweating in that position for that amount of time, I gladly took a 30% pay cut to be an individual contributor again.