I think you've ignored Pike's personal journey through this first season, he's essentially gone through the stages of grief and arrived at acceptance, even if it took meeting himself to complete the arc. He's been shown what happens if he does try to avoid his fate and knows that it's best for things to unfold as it should, so he seems to have accepted that, though the bit with Number One at the end sets the stage for a new "quest".
I think you've ignored Pike's personal journey through this first season, he's essentially gone through the stages of grief and arrived at acceptance, even if it took meeting himself to complete the arc. He's been shown what happens if he does try to avoid his fate and knows that it's best for things to unfold as it should, so he seems to have accepted that, though the bit with Number One at the end sets the stage for a new "quest".