EDIT: Joren posted while I was writing.
Actually, it leaves the GC in a much better position. The subfaction leaders don't have room to squabble cause if they do, the GC government (which is much stronger now) can put an end to it.
What I'm proposing is a reworking of the GC along the lines of the US government (or what it was supposed to be). While it's not the most efficient form of government, nor the most effective, it is a heck of a lot stronger than any other democracy out there (besides maybe Britain and Israel).