It's fine to feel that way, but it's not a particularly effective approach in my opinion and in fact quite the opposite of what I look for in a manager. A good manager manages people; they understand people's strengths, weaknesses, goals, how to motivate and reward people, how to resolve potential conflicts, how to delegate, and how to help people grow. These are all people things. People are not robots which is exactly why they need to be managed. After all you typically do not manage robots, the point of using robots is that they're autonomous.
Problems are not things you really want to manage, maybe in the short run you can try to manage a problem, but ultimately the goal is to solve a problem as opposed to managing it. The goal of a manager is to assemble a team of people who can work together to solve problems.
Your issue is conflating management with superiority, you seem to think that someone who coaches a basketball team feels superior to its players. That couldn't be further from the truth. While Michael Jordan's coach was in his time a competent basketball player, he would never claim to have ever been better than Michael Jordan, and yet both he and Michael Jordan had an excellent working relationship without either of them feeling superior to the other [1].
The issue you have about superiority has nothing to do with solving problems or managing people. You could be a lawyer working entirely independently from developers and feel you are superior to them (or vice-versa). A good manager can cross multiple projects and multiple problems, because a good manager understands people first and foremost and lets competent people work on solving problems, as opposed to trying to manage problems.
[1] https://www.netflix.com/title/80203144