with racing bmx as a kid and using flat pedals for about the first 22 years of biking i remember riding on the arches of my feet.
having moved onto spds from that point onwards and then using both flat pedals and spds up until this day.. i have found that i now race on flats using the ball of the foot at a bmx track.I start off placing the foot over the axle on the gate definately with the ball over the axle.if a foot comes off then it would probably get throw back on closer to the arch but with what im aware of.. nowhere near bang on over the arch like when i was a kid.
i like the feel of first straight sprints on the ball of the foot over the axle on flat pedals. it feels like you can wrap the foot at the lowest point of the stroke to aid the upstroke.this feels crap when you try it on the arches.. probably because the amount of movement between the ankles pivot point(?!) to the axle under the arch.. in comparison to the ankle pivot point to the ball of the foot is quite a diffrence in such a short distance.
try this: place yer index finger across the arch of the foot and move the ankle up and down thru its limits..
now try it with the finger over the ball of the foot and work the ankle. see how much more scope you have?
you were given ankles.. use them!