You could also shape the line to fit the shape of the hand: 5-4-2-1. This is what Chopin, Liszt, et al would do.Pedagogically, I wouldn't play it the way the book has it simply because the arm is treated as dead weight. I wouldn't play it your way, either, simply because that doesn't fit the shape of the music to do so. If it were a fast accompaniment, then crossing over the 2 would be preferred, but it's a melody (I'm assuming.)