In these cases, the manager relies on the team, and the IC to get a clear understanding of the root of problems. You don't need to be super technically proficient to understand constraints, but understanding why those constraints exist requires a deep technical understanding, which is provided by the IC and the team. Using this knowledge, the manager has a perspective of the system and how to improve the system, and the manager tries to reason with the organization, trying to share that perspective with them.
The manager also relies on the IC to do spikes or POC's (or relies on the IC to select a crack team which have a good chance of success).
Most often, the IC has no interest in being in non-technial meetings all day, but the manager does. The manager loves working with other managers + product and helping them understand the issue, while the IC doesn't. The IC wants to spend most of their time on resolving technical issues, thinking deeply about the future and upcoming projects.
All of this to say: they're not exclusive, and both are required for successful teams. BUT, the idea that a technical manager needs to be super technical is not something I agree with.