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There are many ways to invade a planet of humans. That is to say, the invasion’s goal is not the eradication of the people but instead the conquest of them. Such an objective of course it not one which can be achieved with ease, unless one really takes into consideration what they are getting into.
When facing a central authority, such as an enemy government, it is a given that you put all of your resources into the elimination of the central location. When the head is chopped off the organization than it becomes fragmented and more willing to come about negotiations as a body of people. After all, whoever became the next head of the organization would be exposed unless war was to end. In addition to this, such an organization naturally is inclined towards law and order instead of anarchy.
If someone targeted the Emperor of the Imperium, for instance, and succeeded in killing him. The Imperium will either fall apart or become a shade of its former self as few are willing to take the position of someone so great and powerful.
Which was the reason that a coalition like the one the east had become was so dangerous.
They are a decentralized authority with their own interests and desires among each of them. Like a pit of snakes if you kill only one snake another is there to take its place. In addition to that however they cannot really bring upon you a coup de grace as their decentralized manner makes it nearly impossible for them to mount adequate offensives against a more centralized power.
Such is the reason Olympia had been in a Cold War even after the announcement of Perturabo’s arrival. The East cannot fight without accidently overextending itself.
So how can one destroy an organization like this one? Where the heads of state are equal to one another and that there are hundreds of them?
That would be, of course, to strike at them while they were sleeping. Before they could run away into their caves that could be used as a defensive chokepoint to force a more even war footing. After all, while Astartes are indeed many times more powerful than a mortal man if enough lasguns are being shot in their direction their death is a matter of time.
So they all needed to be taken out in the same moment. Just as the fabled hero Heraclas sliced all the heads of the Hydra in a single stroke that needed to be done against the East.