This isn't the nomenclature I'd use. What you describe as a "Technical EM" is what I'd call a "Tech Lead", who doesn't have people management responsibilities (things like 1:1s, recruiting, growth and success of the team, etc) and focuses solely on the technical execution of a team. In my book an EM is always responsible for those people management things, and I'd use "Technical EM" to describe an EM who secondarily takes on some or all Tech Lead responsibilities, directly contributes code, etc.
I've reported for years to EMs who didn't code, and they were just pointy-haired bosses: coming up with ways to manipulate people to make progress quicker, writing performance reviews mostly based on other people's input (why, then, couldn't those people write the reviews themselves?), not understanding engineering realities like some tasks being unknown, demanding ironclad estimates, judging based on appearance rather than substance (or a mix of substance and appearance), and so on. They were just overhead.
The managers I respected were all TLs who were the most important engineer on the project.
Going back to your point, the TL would be the best person to evaluate the engineers who work under them. 1:1s, growth discussions, etc should all be conducted with someone who knows your work intimately, which means the TL. Which means the TL is a manager.
There's still room for EMs to be more technical or more people/coordination-oriented. A technical EM would take responsibility for a smaller area (backend) and go deep technically into it, having the most impact as an individual contributor, knowing all the code, being able to debug any part of the system, being the go to person for everything in that area. Everyone in the backend would report to him.
An EM can also decide to be focused more on people/coordination. They'd take responsibility for a bigger area (backend, frontend, iOS and Android) and go wide rather than deep. If you ask them how to debug an iOS app that crashes in the background, they may not be the best person for that.
