In companies doing this well, the high-level engineer doesn't report to the immediate team lead, but reports to the same director that lead does. Or VP vs director for even-higher-level engineers vs higher-level managers.
That structure, more than the title, is what shows you if you're really on an equivalent track.
There is nothing special about software engineering as a technical track this way. There is no one way to set up an organization. To a large degree they are how they actually work (i.e. not what's on paper).
This balance has been an issue in managing technical teams for about as long as that has been a thing, which is a lot longer than software has been a thing. There is a fundamental tension though, in that the focus you need to maintain expertise in your field contends with the breadth you need to understand the context well enough to make good decisions.
I suspect the real reason that you don't see more of it in practice is that it's actually really hard to continue to do both well at a very high level, and it's also organizationally hard to do.
I'm trying to make sense of the rest of your post, but it uses a lot of pronouns that don't appear to reference anything.
I agree software has more leverage, sometimes but we are talking here about how decision making power is distributed in a company.
Regardless about how much impact the IC technical output can have that is about how. The skills & information needed to make good decisions about what and when are different.
Unfortunately, being highly effective at both requires spending time and focus in ways that are somewhat mutually exclusive, which makes this quite hard.