A coincidence that bothers me

[FoldALot.]

Also, about the Proto-Moon/Earth collision being a "very lucky shot":

Sure, if it happened differently we would not be living on this this planet right now.
But, the fact that we ARE living on this planet right now means the collision had to happen exactly as it was. Else there would be no one here able to notice the "lucky shot" and discuss about it.
Therefore, we know nothing about how random the event actually was. Collisions will have occured millions and millions of times in the universe, but if this configuration is the only one that can lead to intelligent life then it will be the only one that gets noticed and analysed.