A huge portion of the original post was about what was chasing them.
"Just not gonna happen" I dissagree with the course your logic went. It was one way to look at it, but certainly not the only way as you implied.
First off... what campaign? There is no campaign in the game, just a backstory and, as you said, really cool space battles.
Second... The univers is large, very very large. That means alot of time to hop out a certain distance and make homes for a few generations before they start to gather resources again before running.
Speaking of which, that's one of the reasons why they won't be working together, they all need what they can get.
They also wouldn't trust each other, the other reason they wouldn't unite, their views of what's "right" is too different. The TEC think Advent are heretical and immoral, and the Vasari are slavers. The Vasari are slavers above all other races and would not deem to work with the TEC or the Advent. The Advent want revenge on the TEC and after they were wronged by the TEC they likely wouldn't stand the Vasari control over them.
Actually, they never even have to adress the issue other than another two lines of narative in the next intro movie.
Narative: "The Vasari's mistake had caught up to us all, and now we all have to pay for their culture of war." Then add something about fighting over resources and the Advent following the TEC to fulfill vengeance, yada yada about the Vasari using them all as slaves to help themselves survive... cut to the main menu.
And they don't even have to do that, it (the blast) could be 5,000 years away from reaching where the 3 races are now and it could be completely ignored.
"Wont be fun to play." Maybe not to you... but it sounds fun to me.
They make any games they want, games are now intelligent and have very different goals, settings, and gameplay styles, even between sequels of the same name.