I understand that many large institutions are constructed in a mechanism you describe. In many cases, these managers are technical enough that they can substitute any individual working under them. There are also many cases where they are not sufficiently technical.
Nonetheless, if a manager’s purpose tailored towards prioritizing, fighting for projects, and assisting ICs career growth, I am not convinced that that manager is necessary as I am not seeing his value. Prioritization ought to be intrinsic for everyone and is more a collaborative choice, no? Why does a single individual (manager) decide priority?
Often ICs don't have the context necessary to contribute much to the conversation once it leaves the sphere of influence of the team they're on--and more importantly most of them don't want to acquire that context, often because they view it as inferior work that is beneath them. They don't see value in management because they can't see past their own egos and myopia.
Plus, at the end of the data, a good manager should aim to hire people smarter and better than them. If they can step in for those people quickly then they're not hiring better or smarter people which is a problem. A first line manager should understand what people do but that is different from being able to do their job to the same level.