All that stuff used to bother me, but you just really gotta buy into the "fate" stuff. Yes, there's no way in hell all of the pieces should fall together like that. But think of it this way. Nero and Spock's arrival forked the timeline. As best as it can, the timeline is trying to course-correct since then, trying to put itself back "the right way." There's obviously only so much it can do when Vulcan was destroyed, but the deus ex machina moments are almost literally that: "god" (the universe) trying to put things back the way they were supposed to be.
It's a bit strained, but I think that's really the idea the story's trying to put forth. "Timeline resistant to change concocts unlikely events in attempt to course-correct" as a long-winded synonym for fate.