the Trek District looks like an awesome belt-drive singlespeed, but again, I'd be reluctant to use a carbon belt drive on a fixed gear. For a nice singlespeed commuter bike, I think it's a great idea, just because you don't have to worry about the maintenance as well as the mess that comes along with lubed up metal drivetrains. It makes sense for a no-mess utilitarian bike, but I think for a fixed gear/track it wouldn't be worth it. Most of us don't care too much about getting grease on our pants, and we expect to maintain a chain by lubing it up regularly and cleaning the drivetrain.

There's just a lot of stress put on a fixed gear drive train compared to a singlespeed (resisting, backpedaling, skidding, tight fresh barspinz) that I don't think it would be practical, or safe.