IMO, they probably were semi-autonomous because none of them could virtually survive without the others. It's quite possible, IMO, that during the Reconstruction period the classic "I give you food, you give me weapons" helped a lot. Our info on canon planets are poor, so we don't know what kind of resources each system could rely on.
For example, the normal Prometheus became nearly impossible to produce after the collapse of the Sol jump node, so the GTVA came out with the Prometheus R. This means that, eventually, GTA systems other than Sol did not have a considerable number of exploitable gas giants.