I have learned, through much trial & error, that proper paint correction takes more steps, and a more aggressive approach, than at first seems necessary---and some car care products actually 'hide' issues in paint rather than remove them.
To remove clearly visible scratches, you've got to take the paint down enough in depth to actually level the unscratched surface with the scratches. While that depth is not quite as much as you might fear, it's more than most people know how to get down to until they work with the proper product (compound), DA polisher and technique. But once you know and become comfortable with these pieces of the puzzle, it's suddenly easy.