I think birds (all flying ones, at least) seek the highest level available because they are prey animals and have evolved to seek protection in the heights. I'd bet money that most of the birds connected to our forum roost on the highest available perch in the their cages.
I don't know where the theory of a bird feeling 'dominant' came from. My birds don't dominate me, but they all love to get up on top of the bookshelves or the fridge and just chill there (no pun intended).

You only have to look at them to know for certain that birds just love being up high. Dommie used to raise his hat, extend his wings and virtually sing for the joy of being up high! Rosetta does something very similar, now that she's found she can alight on top of my quilting cupboard. I think they feel a real sense of well-being up high, just as they feel vulnerable on the ground.
Answering my own question: pecking order! A Norwegian bloke proposed the theory of 'Pecking Order' in the 1920s. He observed domestic chickens seemed to show a hierarchy of dominance based on which chook had the strongest peck. Naturally, the dominant rooster held the top spot and a complicated hierarchy tumbled down from him.
Thing is, Schjelderup-Ebbe studied chickens. Their social hierarchies are not really similar to those of other birds (like parrots or albatrosses or moorhens etc). I don't think it's reasonable to ascribe the dominance theory to other species because the entire social set-ups are so variable. Other forces are at play, notably predator-avoidance, foraging, water discovery, roosting (communal or otherwise) and so on.
Bird behaviour is a fascinating area of study and we still know so little about why birds do what they do. Researchers like Tinbergen and Lorenz kept the ball rolling and made some flabbergasting discoveries in the 1930s, notably the complex courtship rituals of seagulls and the responses of capercaillie chicks to a silhouette of a hawk/goose suspended above them.
I'm aware of plenty of behavioural studies being conducted on various sea birds and endangered species, but AFAIA not many people are really delving into the reason parrots do stuff. My own observations of wild flocks would suggest that parrots *don't* involve a dominance hierarchy, but depend more on pair-bonding for security and confidence. I'd love to hear of any studies that might confirm or dispel that idea.
Sorry for the essay. I hope you can tell this is a subject dear to my heart and I would *so* love to hear of other people's observations as well.