To me, it's about control. I recently started riding fixed after 2 decades of riding 'regular' freewheeled bikes. I went riding with my kids (6 and 9). If you've ever went riding with kids you know how important control is. My 6 year old will stop or turn on a dime for reasons that only make sense in his little head.
When riding fixed I was able to moderate my speed with amazing ability. My 6 year-old's antics were insignificant. I wasn't ever coasting so I never had to grab my brakes unexpectedly. I could do little adjustments with my speed and only grab the brakes when I had to. I was surprised. I had done a few longer rides and enjoyed the fixed difference but only after riding in a more challenginrg environment did I really realize how fixed changed the ride.
I'm no messenger. But after that ride it made me realize why many messengers ride fixed. They need that level of control to navigate the everyday madness of the streets.
Try it, you'll see.