If you ride serious hills, you will find that brake hoods are really nice for climbing. If you are going to put on hoods. it isn't much extra weight, etc. to run cables and a rear caliper. (Especially since hoods are usually sold in sets and include levers. Likewise calipers are usually sold in pairs.)

And downhill at high speed, the rear brake is really nice for bleeding off speed and keeping your RPM under control. We can be talking RPMs that the rest of the world will say cannot be done. I've done close to 50 mph (many years ago when I was young, recently post racing, riding my post accident years for my sanity and descending Oakland, CA's Juaquin Miller on a 42-17. That's well over 200 RPM.

Plus, when it comes to real downhills, redundancy in stopping is never a bad thing. And once you hit 40 mph, forget about using your legs! Suppose anything happens to your front brake.

As far as problems of a rear brake on a fix gear? Well they have not shown up for me in my first 94,000 miles. Not saying there aren't any. I'll keep riding fixed and report back when I see them.

Ben