I don't think that's accurate that bike messengers use straps nowadays.

They're the worst of everything...
- worse to get your foot out in an emergency than flats or clipless
- getting back in at a stop is pain because the strap rotates down to the ground and you have to flip it back up
- clipless doesn't even get you an efficiency or speed benefit in lab tests so straps are even less likely to

I wouldn't recommend straps to anyone I know, it's flats (with five ten shoes if you want top grip) or clipless. Both are good systems, straps have drawbacks without having advantages.