It’s also routine in VAQ land (especially because our CDRE essentially acts as the CAG for the four expeditionary squadrons). In answer to the OP’s previous question, I think the best way to put it would be that aviators on the CVN track don’t get to fly as frequently as CAG/DCAG, but it’s still a tour that allows for flying. In theory, aviators (both CAG and CVN CO background) can still fly after their CVN CO tour if they end up commanding a CSG. One of my CSG admirals flew several times a week during work ups and deployment. However, I’m not aware of any other flag officer billets that allow regular opportunities to fly.
And yes, the instructors in nuke school are junior to the O-5s/O-6s that are on the CVN track.