Basically the answer to your question is that too little of any problem is engineering to justify someone experienced remaining as just an engineer. As you get more senior, you should be knowledgeable and experienced enough to be able to coordinate the efforts of other engineers and mentor (or facilitate mentoring of) junior members of the team. And you should be able to cooperate (or battle) with other sections of your organization for resources and to convey progress on your projects.
Everyone would like the person doing the above to be someone intimately familiar with and good at the work they're managing, or else everyone is pointy haired boss and we all have to complain about how MBAs are ruining our lives...
> As you get more senior, you should be knowledgeable and experienced enough to be able to coordinate the efforts of other engineers and mentor (or facilitate mentoring of) junior members of the team. And you should be able to cooperate (or battle) with other sections of your organization for resources and to convey progress on your projects.
I agree that those tasks are important, but none of them require being a manager who is formally someone's boss (hires, fires, does performance reviews, deals with HR issues, etc.). I didn't like being peoples' boss, so I stepped down from my management job years ago to become a developer again. But as a very senior developer, I've done all of those other things (mentoring, coordination, cooperation, etc.).
Just because you have the ability to do all those things you listed doesn’t mean you need to do them. It’s a valid choice to continue the relatively lower stress job of a software engineer.
Everyone would like the person doing the above to be someone intimately familiar with and good at the work they're managing, or else everyone is pointy haired boss and we all have to complain about how MBAs are ruining our lives...