I appreciate you don’t want to move job. However you also said
But even if they moved sideways to do an equivalent level role to me in a different section, the reality is they'd take a very strong input still in what I / my team do, just because of the specialist niche we are in. It's really not ideal.
You can’t have it both ways. This person, if they are well thought of, will progress. Especially if the company doesn’t want them to leave. As you don’t want to move jobs, there has to be an alternative progression route. So you may need accept this person will move to your level in a different section and will have input.
What’s the alternative? That everyone below you must leave if they want to progress. That’s not your company culture. They want internal progression.
I am sceptical that a successful male leader would be told to dispose of himself so an aggressive junior could have his job.
No one is suggesting Op dispose of herself to give her job to someone else. But this person wants to progress. The company wants people to progress. Op can choose not to progress their own career, but that doesn’t mean people behind her can’t progress their own. She will need to accept it’s likely this person will move to her level in a different section and will have input on her team, as that’s the set up. The other sections have input in her area. Then they may progress beyond that.
Whats the alternative? That anyone working for Op works for her for a bit then leaves?