The endorsement of such a simplification as the alpha ideal can be hurtful, not against truth but against what is generally beneficial to society. As alpha as a term becomes accepted it becomes, in itself, a positive. To be alpha is good. This is because many of the traits included in the constellation ARE good. Confidence, competence, a willingness to lead, aggressiveness when appropriate etc. But many others traits are not good, and are not helpful to society, ruthlessness, dishonesty, these things promote dominance but hurt the whole. They are endorsed and encouraged as the idea of alpha is endorsed and encouraged. To use the term, to accept the term, is the same as using and accepting the N word. It should not be used not because it is "untrue", so to speak, but because it is harmful, has negative results.
In short. We have no reason to say that the ideal of alpha is "true" or useful, or accurate, while at the same time we have good reason to think the endorsement of it isnt helpful. Why use something both untrue and unhelpful?