you are confusing alpha traits with jerk traits.
alpha = natural leader (with all the qualities of a leader)
beta = follower (with the frustrations, and limitations of followers)
an alpha is not careless, he is independent, dominant, and in general a protector. he is the main man, and he knows it, he knows others know it, so he feels no need to show off. a leader does need validation for his actions, doesn't care about it, but being a careless jerk is actually the beta trait.
the betas need constant validations from others, make excuses to be clingy, manipulative and in general they are those who are more selfish.
that said, alpha, beta etc are just labels. no need to jump on them every time, and labeling everything with the greek alphabet. it is a stupid way to live.