I've wondered about this myself too. I've never seen a close up photo and seen anyone at the velodrome that does not just wrap the strap around the pedal and shoe the way you described (even then, I've only seen two guys do it.
It occurs to me, though, that if you had two small steel loops, you could bend them open, put them around the spindle inside the pedal cage, then bend them closed. Then thread the strap through them underneath the cage.
It would seem that you really just need something to hold it on there for you so you can stick you foot in, snap in, then tighten down.