We may be talking about different levels of management here. A manager should not be making technical decisions, they should have team leads and architects who do that. It's their job to manage the team, interface with the business, prioritise work and give cover to the team so they can get on with it.
I guess if you have a manager who is making technical decisions, they are really a hybrid manager/contributor role. Maybe that works better in smaller organisations.
Then what exactly is the non technical manager's added value?
He has no experience to lead the team in high pressure situations. Like production being down.
He can't truly have a first person understanding of the work of the people who he manages. He has to rely upon others to tell him who's good and who's bad. That sets up a pecking order.
He can't help or mentor engineers with design decisions, or provide a historical context.
He doesn't understand the technology so there's an immediate communication and knowledge barrier that has to be overcome between him and his directs.
He doesn't feel the pain of a bad decision, because he's not coding it, and he can't emphasize with them since he doesn't code.
He tends to push feature development without fixing technical debt. Again that's pain he personally doesn't feel.
To me, the role you are describing is a principal engineer or team lead, not a manager.
Simply not true however that a good manager can't lead the team in a high pressure situation. I'd say that exactly what a good manager could do well. Obviously they won't be making overtly technical decisions, that's what you are for. They can make business decisions, provide cover, get resources, communicate to other stakeholders... All the bits that need doing but would be a huge hassle for the techies who are trying to fix the issue.
Not everything of value is technical. That you don't see the value is either because you have great managers shielding from having to deal with all that, or you have always worked in a place that combines management and technical responsibilities (which I never have except for very small companies).
I wouldn't call what I'm describing as product management, although it's possible they could do general management too.
I guess if you have a manager who is making technical decisions, they are really a hybrid manager/contributor role. Maybe that works better in smaller organisations.