A nice dream, but that describes every war we've fought so far. They still seem to happen juuuuust fine.
Only if you conveniently ignore the next line.
This is, at least as far as the GTVA would be concerned, brother against brother. The entire opening narration of FS2 basically craps all over your statement.
Sol is a logical place to draw a new conflict, but that does not mean the conflict is going to be human against human. It's not an FS game without Shivans, and we've pretty well exhausted the Shivans-from-nowhere-in-the-middle-of-something-else technique by the end of FS2. They probably wouldn't have pulled it again. FS3 would more likely open with the Shivans already in play somehow, for one side of the exchange or for the other. Perhaps an "out of Sol" to save the remainder of the Terran race. Perhaps an "into Sol" to save Earth. Either option makes far more sense in terms of telling a new story and a final conclusion to the Shivan conflict that has dominated FS storytelling.
INFR1 came closest to a reasonable justification for a GTVA-Sol war by having Sol start it.
The justifications present in every post-Capella campaign for the various circumstances they present are far from silly; though I understand your points about First Fleet, most of the aforementioned fiction handles it pretty neatly.
Oh sure, S:AH is a great campaign to play, but it and INFA (which isn't) are simple handwaves ("we're here to save our Neptunian brothers!" Well that's great, but where the **** did you come from?) that really make no sense about how Sol got that way. Very few other campaigns present a view of a war in Sol aside from TVWP, which doesn't touch on this subject.