I am learning a "Hard days night" by the beatles which is in G mixolydian mode or C major. In the score I have of this song the writer notated the song in G major and used accidentals on the notes that are not part of the G major scale. Why couldn't they have just used C major as the home key as all the notes pertain to that key? Is this because the song keeps going back to that G chord? If this is the reason it seems silly because you could have a C major song with these chords in a bridge and then it would be notated in C major.

I am learning "A Hard Day's Night" by the Beatles which is in G Mixolydian mode or C major. In the score I have of this song the writer notated the song in G major and used accidentals on the notes that are not part of the G major scale. Why couldn't they have just used C major as the home key as all the notes pertain to that key? 

Is this because the song keeps going back to that G chord? If this is the reason, it seems silly, because you could have a C major song with these chords in a bridge, and then it would be notated in C major.