Seems like it depends on how you define ‘manager’. Your lead developer is what I would call a manager. In my experience, most managers have been team leads who set priorities for the group, help arbitrate technical decisions, advocates for more resources for their team, negotiates with other teams over who will do what work and take responsibility for which parts of the system, advocate for promotions for their team members, and deal with underperforming team members.
I don’t know how a large company could function without that role. If you have 200 developers working on 100 different projects.... who is deciding what to work on? Who is deciding how many people should work on what? Those people are managers.
I like how Engineering Manager is defined in "The Managers Path" -- which is what you are describing. They shoud be someone who does an occassional bug fix to maintain a boots on the ground approach, but is spending 95% of their time on the items you listed. I think one issue w/ Managers is that we get manager's who should be at this technical level, but are instead so hands off (or fully non-technical) they can't even reason (or delegate) priorities when architecture or tech debt is involved. To be fair, I have worked with fully non technical managers who had a good understanding of how much time to allot towards architecture, refactoring, etc. But those are rare.
I don’t know how a large company could function without that role. If you have 200 developers working on 100 different projects.... who is deciding what to work on? Who is deciding how many people should work on what? Those people are managers.