but in most group scenarios there would be some people exerting much more influence than the others 

Sure, but that is what is meant by group dynamics. And it usually isn't one dimensional.

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.