Owns the requirements and the interfaces on a programme too big for any one specialist to hold in their head.

Nobody designs an entire aircraft, or an entire car, or an entire factory. A systems engineer is the person who makes sure the pieces different specialists design actually fit together: turning a customer requirement into something traceable and testable, defining the interfaces between subsystems before two teams find out the hard way that they assumed different things, and running the verification that proves the finished thing does what it was asked to do.
The usual route: a few years designing one part of something, then moving outward into how it all fits.
A direct route, and considerably stronger when it follows real hands-on design experience.
No published projectionSystems engineers are counted under whichever base discipline they trained in (aerospace, mechanical, electrical) rather than as their own occupation. The Handbook has no entry for systems engineering itself, so this profile quotes no figure rather than borrowing a neighbour’s.
You are responsible for the whole thing working and an expert in none of its parts, which takes real confidence to sit with. A requirement written ambiguously in year one can cost a redesign in year four, long after whoever wrote it has moved on. And a review where six specialists each defend their own subsystem is where the job actually happens, chairing it well is a skill nobody teaches in an engineering degree.