I don't see any problem with fingering the chord the way you describe. I, too, learned to play the G with my pinkie hanging there doing nothing. I think the chord is pictured that way in most beginner's manuals because it's a little easier to do. But in the long run, I think good instructors ought to teach it the way you describe, with the index finger free to do so much. I couldn't play half the things I play if I had to play the chord the old way.