Sure, but now we're talking about a programmer analog of Maslow's hierarchy of needs.

The first trait of a manager in high tech (whether professor or product manager) has to be technical competence.

That trait is not usually sufficient to be a good manager. But I think it's necessary (you seem to disagree?)

I would disagree. Many of the good managers I've worked under haven't had much coding experience. What they have had is the ability to trust the team to get them briefed on technical issues as they come up.

I could see this being different in other environments (eg I can't imagine a research team manager not being an alpha geek) but for most corporate environments there are a lot of other skills I'd look for before technical competence.

For example, one of my inspirations early in my career was an EPM (engineering project manager in the company's lingo) who had zero technical background. What she did have was an amazing ability to listen to everyone involved in the project, pick out the chains of dependencies, negotiate schedules with us, follow up relentlessly on any open questions and summarize what we'd just said better than we ever could. She made a massive difference, and the team's productivity dropped like a stone when someone less talented took over.