Well, as I mentioned 400 posts or so ago, Cable showed Scott a vision of an apocalyptic future and told him that this would be the result if he let the Avengers take Hope. Fact. Also, Fact-- Even before the Phoenix arrived, Hope had already re-ignited the mutant race, but just at a much slower pace than after she hosted the Phoenix.
Put those facts together, and I still say Cyclops was more than justified in his belief/faith that Hope would restore the mutant race. And don't forget-- he was right.