A rich Alpha Bitch would not be immune to the desire to have others demonstrate her dominance by bringing her gifts. And a less-than-rich Alpha Bitch can occur through sheer force of personality; most commonly, but not always, this person will be an oldest or youngest child in a large somewhat-dysfunctional family.
On the other hand, a person who obviously has what it takes to be Alpha Bitch and obviously rejects the role (such as Susan) weakens the power of the role. This is good for other students who can't, or don't want to, play those games.
Much the same is true on the male side, albeit manifesting slightly differently. Elliot, being obviously athletic (quite possibly one of the top athletes in the school) and apparently having little interest in school sports (plus having an obvious nerd and a couple of brainy non-cheerleader girls as his best friends), makes things a lot easier for non-jock/non-cheerleader schoolmates. Even without him making any effort to do so.