But why would fate make sure Kirk and his TOS season 2+ crew united, and not the "proper" crew of Pike or even Kirk's "Where No Man..." crew? And why would fate allow Amanda and planet Vulcan to die?
You're asking about fate like it's a reasonable thing. The simple answer is that those things were not fated to happen. The uniting of the cast of season 2 in all of their same positions in a different time despite the seeming improbability is fate.
When such great coincidences occur, that's when people start to question if there's something more to it. You can either assume that there's some sort of in-universe mumbo jumbo to explain it (like Orci's poor attempt), or you can just accept that it happened that way because the writers wanted it to happen that way without any concern about if it makes sense. Neither of those are very palatable options for me.
maybe the universe is ensuring it's own survival by uniting Kirk's crew at all costs.
Again, that would be fate. I never really felt like Kirk or Picard or anyone on Star Trek were the only ones who could save the day in specific circumstances.