Aside from
subsector dukes...
[There really is too little information about the Imperial system in early CT material to say much about how it works, so I'm abandoning the restriction of only going by what it says.]
The Imperial Nobility is not just one homogenous group. The one trait they all have in common, that of having a seat in the Imperial Moot, they don't actually all have in common -- younger children of peers don't sit on the Moot (Nor do heirs, but they will eventually). High nobles have built-in duties -- dukes are a cross between Imperial governors and pocket emperors (in one sense every duchy is an empire of its member worlds). Lesser high nobles act (I believe) like a sort ombudsmen. They step in when the normal Imperial bureaucracy is unable to cope either from deliberate abuse or inadequacy.
But that leaves all the honor nobles and the younger children of nobles. I think the Imperial nobility functions as a labor pool. Some enter the Imperial bureaucracy; some enter the Imperial services. According to
GT:Nobles, the top levels of Imperial jobs require a minimum noble rank. At the lower levels, competent commoners can be given baronetcies or lifetime peerages, but for the jobs that require higher noble titles, existing nobles are chosen almost every time.
An old aphorism (that I made up myself) says that "The oldest child enters the Bureaucracy; the second child enters the Navy; the third child enters the Army; and the fourth child enters the Scouts". Of course, this is not always true; some go into civilian life as corporate and (especially) megacorporate managers; a few become academics, and some just kick back and enjoy their wealth and priviledges.
So other than high nobles there isn't much power invested in noble status in itself, but noble status opens the door for acquiring positions of power. Really competent commoners can work their way into powerful jobs (and the lower ranks of the nobility), but they have to work twice as hard to get there in twice the time it takes nobles.
Another thing is positions in planetary governments. In theory, the Imperial nobility are separate from planetary government; in practice, planetary rulers, especially hereditary ones, tend to acquire Imperial noble titles. Also, an Imperial noble title carries a lot of prestige, so an honor noble is in a good position to get ahead in planetary politics.
And that's my view.
Hans