As an engineering director, I have an entire organization of teams I'm personally accountable for, and I have to make sure the work that's being planned out meshes well with what all the other teams are also planning. I cannot constantly be pulling in a dozen senior developers into every meeting every day to help me figure things out. I also have my own technical objectives I want to achieve for the company that cut across multiple teams or the entire engineering organization. Most of these considerations are technical in nature, and while a senior IC on one team can help they frankly don't have time to be involved in the whole process -- that would prevent them from succeeding as a senior engineer in their current role.
Under discussion is not the role of a senior engineer, but rather the technical track beyond that point -- roles commonly termed staff, senior staff, distinguished, principal, fellow, or even senior fellow. My core claim is there's more in common between engineering management and these roles than many folks tend to believe and/or realize.
Often an engineering manager is just someone at this level of seniority who also has rock-solid people skills and has been empowered in the organization to actually get bigger things done that cut across teams, though they may not themselves write code anymore.
Certainly I agree with you that not every manager needs to be deeply technical, but I think that for someone who is deeply technical, engineering management can actually be a much more powerful and interesting choice vs. trying to expand your impact without taking on formal leadership responsibility on an IC track.