The originator of the (generic) concept "alpha" (please let us know who this is / who you think this is) has discontinued the term "alpha" (quite an alpha-decision from him, I would say) due to new insights discovered when observing wolves. Alpha does not exist for wolves (presumably)... and in general. To extend just further (why not) the concept gets fully discontinued, due to public pressure, because everything is equal anyway.
You had me until your last sentence. What do you mean that the term is being discontinued due to public pressure? Isn't it natural for concepts to go away if they're found to be inaccurate (ex: phlogiston)? I also don't understand "everything is equal anyway". Could you elaborate?
Since you mention the term in relationship to the public, I actually think that "alpha" as a term to describe someone who is dominant has been doing just fine as a societal meme, despite it being used less among biologists/whomever. In this sense it doesn't seem to be going away at all.
I am being ironic (which is not allowed here, actually) and I am mocking the SJW an PC pressure, which very few but loud proponents shout out on the internet, mainly social media, today. Wishing away things, like not only the concepts, but also the words. But that won't happen and we see an alpha leader / beneficent dictator (for life) rise again (because it just works so well): Elon Musk.
