In other words, I think there are actually humans who are usefully described as "alpha", but they are rare enough that most people will never actually meet one in their lifetimes.
If that is true, thinking about this dynamic as useful in understanding the people they actually do interact with easily becomes misleading.
There are certainly many people who like to think of themselves as "alpha" but invariably in my experience they have been obviously, and demonstrably, wrong.
Maybe not a full blown "alpha" (that would e.g. be their political leaders, CEOs, etc, so they will affect their lives, even if they don't get to meet one as a colleague/friend), but in most group scenarios there would be some people exerting much more influence than the others, even without a higher rank.
but in most group scenarios there would be some people exerting much more influence than the others
What I'm saying is that the alpha/beta modeling of this is lazy and misleading, and better avoided.
A very few politicians and a very few CEOs meet a useful definition of alpha, in my opinion. Your point about rank affecting influence is true, but I think irrelevant to my point.
The "alpha"/"beta" wolf-pack dynamics were debunked a while ago. Packs are typically made up of parents (previously referred to as "alphas") and children (previously referred to as "betas").
Status is definitely important, but the alpha/beta/omega/gamma/delta/greek-anthropomorphism thing is a load of crap.