Something wonky is definitely going on in mission 3, but I'm not sure what. It could be for-counter (I'm still using the default build for the campaign), or it could be something else.
I have "captured" checkpoint #1 in a tech room playthrough of the mission, after all the fighters are destroyed. Some mission events fire after that (Krishna wing jumps in, for example), but the allied cruisers never "get into position"; they reach their waypoints and idle there forever, and the Legion never arrives.
I don't know what I could be doing to make this happen. I'd been playing with different strategies to have as many of my wingmen survive the early part of the mission as possible (so they'd be of greater use during the later parts), which entailed having them mass attack the Shivan fighters one by one, then destroying the Cains once their fighter cover is gone.
Example: Destroy fighter group 1 -> Destroy Cain 1 -> Destroy fighter group 2 -> Destroy Cain 2, etc.
EDIT: I did some testing and was able to reproduce this, though I'm still not entirely sure what's going on.
It looks like if you restore the mission from checkpoint #1 with only one surviving Cain (there may be other variations on this but I haven't tried), and then destroy that Cain, the game "forgets" that this triggers one of your secondary objectives. The Legion never jumps in and the mission never advances.
Note that this weirdness won't happen if you play the mission straight through from the beginning. You have to use the checkpoint for things to bork up.