"Going other places in nuclear" does not mean instantaneously. I don't believe I suggested that an NLO would jump directly to senior management, for example. However, they do frequently seem to wind up there eventually, whether via license class or some other pathway (if they want to leave shift, of course, which many do not).
I've seen former NLOs in all sorts of positions, from Ops / Chemistry / RP / Training / Safety / even Engineering management, all the way up to senior corporate. Again, this is based just on what I've observed at the facilities at which I've worked. At my current utility former NLOs can be found at all levels of the organization.