I think your starting assumption is flawed in several ways.
First, bullying behaviour is not universal - that it is broadley spread in some countries, and not in others, shows that it depends on how society and adults react to it, and how much/little value society places on harmony / getting along, or what qualities are respected (machoness or smartness.
Second, Bullies are generally not smarter than their victims. Not because of stereotype, but according to sociological and psychological research. Partly bullying behaviour is lack of empathy and carelessness, but often it’s also self-esteem issues: the easiest way to feel good about yourself is picking on people perceived as inferior.
Third, what actually was an evolutionary advantage for pre-humans and humans was cooperation. Regardless of the myth of “the strongest survive” and “it’s everybody against everybody, every man for himself”, people who really understand evolution and study human apes and human groups will tell you that the only way to survive against fierce predators is cooperation (that’s how chimps deal with leopards: all together throw sticks and stones; rugged individuals are eaten).
That’s why language is such an advantage: it allows cooperation.
You can also see two different strategies of group behaviour when you compare different human ape groups: chimps fight among themselves; bonobos make sex to keep peace.
This leads me to alpha male: true, having a hierarchy with an alpha at the top is almost hard-wired into humans from our ancestors. But that doesn’t mean that the alpha bullies the beta, the beta bullies the next lower ones, activly. Studies have shown that good alphas - better survival for the group, less challenges = less stress, longer life - have a harmonic wise leadership. Yes, if one individual steps out of his place in the line - eats food before the alpha has had his share for example - the alpha will tell him to cut it out; and if somebody challenges the alpha, there will be a warning, then a fight.
But activly making life miserable for the lower orders, which is what bullying really means, is seldom seen in good succesful groups. It’s not a good long-term strategy.
The other reason we see it often in humans, along with racism and similar, is that the easiest and quickest way to achieve group cohesion is to pick on the outsider (esp. if they are perceived as threat). That this works well doesn’t mean it’s a good strategy, however.