BP does deal with this issue, and it makes the case that the war is a necessary evil to stop the processes that are inevitable due to the intersection between Sol's own ideologies and soft power and GTVA's objectives.
That's one possible answer out of a million. If you consider that Sol has instead imploded in downright depression, tribal warfare and, why not, nuclear war, the variables would rather shift in many different directions. If you envision however that Sol is more or less OK and the outer colonies are really an amazing economic and social miracle due to some unexpected technological changes or whatever, then a massive migration should be expected from Sol to Delta Serpentis, etc. The Power structures all depend on these much more fundamental vectors, and as we are seeing, they can vary wildly as the writer will want them to.