It sounds like you're saying that top-tier engineers are not generally qualified in terms of non-technical requirements, and I don't know that this assertion is justified.
From my perspective, as a relatively new technical manager who also spent years as an engineer working with technical managers, it's not only about empathy but also about having a thorough understanding of, or at least an accurate intuition around the subject matter. When I was working as an engineer, what I often found frustrating about working with non-technical managers is that they often work on the wrong set of parameters. Discussions often revolve around details which are not really important to the success of the project, or are relevant to the work, and often the team is led down a more difficult path than is necessary because requirements are set in the wrong terms.
I think it's possible to compensate to some degree with empathy and people skills, but it's hard to compete with having the experience and speaking the language.