As one who has been a turboprop captain and now a jet FO, it is cearly better and infinitely more satisfying to 'run your own show'. You have to see the RHS as a vital and necessary apprenticeship from which much could and should be gleaned. Nevertheless, it is a great moment when someone believes in you sufficiently to put you in the left seat of a big shiny jet. I would say that it is normal, and indeed essential, for any aspiring pilot to want to be captain one day. The lack of such desire shows something fundamentally lacking. It would also be fair to say that there is no company I have ever heard of who would take on a new pilot if they did not believe that in time he/she would have a strong likeliehood of being in command of their own aircraft. Whether or not they enjoy the left seat when they get it is another matter.
There are all sorts of apocryphal tales of people who should have been promoted but were not. However, the bottom line is that if you aspire to become a commercial pilot then you must display command potential. If you do not, you will quite rightly not be offered employment.