well....regarding alpha, when you say that alpha is unwilling, this gives the impression either that alpha is lazy, or lacks drive. in short, saying alpha is unwilling reflects a beta bias. alpha's energies are directed toward intellectual production and innovation, data gathering, testing, tinkering. you can't engage in this type of activity fully if you are thinking about starting in with the establishment, planning strategies, and pushing people to take risks. all of alpha energy goes towards inventing their products. alpha endows beta with ideology, innovations, and new tools to drive a cause.
the same as beta can't be rabble rousing, getting things started, and throwing out the old stuff and at the same time be concerned with the efficiency and production and profit that gamma is all about. you can't do both at once.
i also don't think beta's primary mission is to destroy. their mission is to get the new ideology going in practical application. they may throw out the old, but more likely they are focusing attention on the new and the new way to do the new. i think this because people are much more attracted to doing something rather to not doing something. i think beta emotionally destroys the old way through propaganda and Fe-infused leadership, but that's in juxtaposition to the new way. part of the beta motivation and agenda is to overturn the delta aristocratic leadership way of doing things to match the beta aristocratic style. but this is a different thing than generalized destruction....more specific.
lastly gamma seems to be concerned with profit and efficiency. how to make money off the new way but also how to bring the new way to everyone in the most expedient way possible. competition is also a strong element in gamma and the only rules that apply are those of personal relationships. otherwise, all bets are off and it's dog eat dog for the money and power. there was a saying in the 80's: greed is good. while i would hesitate to put that phrase in a formal description, in a way it captures gamma philosophy. free-wheeling enterprise and entrepeneurship reign in a gamma phase.
if you feel like it, it would be interesting to look at the rings of benefit and supervision. the right ring follows the progression from delta that you describe...how do you describe the left ring of social progress?