How often have I heard "you’re at a point in your career now where a people manager will only hinder you" to justify not being capable of supporting me.
I think this is a good indication of increased authority/responsibility, but also an easy way to shirk management responsibilities as you said. How much 1:1 management is a VP or CTO going to be doing with a Staff Engineer? Do you really want a VP with all the political nonsense that comes with that type of position to have their own pet engineer they can bother about things?
If you think "Gosh, that person (on another team) sure was rude", that's a question for my manager.
If you think "Gosh, I sure have no idea why that API (from another team) sucks", that's a question for me.
In terms of reporting to my manager it feels more like having a corner-man in the boxing ring than a boss. I fight the fight, they say "Hey you're dropping that right hand on your left hook, stop that or you'll get rekt. Here's some ice". And they spend more time thinking about and navigating politics-like issues in the org than I do, which means I can lean on their expertise when "org stuff" is needed.
I probably have similar or more years of experience than my current EM. The person we both report to, happens to be a true greybeard.
An important part of the job is to “borrow” your boss’s authority and for that to work they need to have some. I’ve seen staff engineers be ineffective because of their boss’s position many times.
Reporting to someone higher than director you start getting too disconnected from on the ground stuff (architecture astronaut syndrome) and lower the ground is all you can see.
It’s refreshing when a company realizes that staff engineers with 15+ years of experience don’t need daily management.
The last 3 companies I've worked for had no juniors and mid-levels, but only seniors and a handful or staff engineers. What staff engineers did on a day-to-day basis was hardly different from what the senior engineers do, besides having more responsibilities and maybe more say over things like architecture. Depending on the company, a staff engineer could be managing or not managing at all. In general, I don't think these title really mean a whole lot, that is unless one is intent on managing specifically.