I'll steer clear of the usual BS replies this board seems to get, and try to offer something of value...
Benefits of leg braking:
It's pretty obvious, but you dont have to use brakes.
no brakes = less weight, less parts, less cost, less things to go wrong.
I can see the point of using a brake if you're starting out, or for emergencies, but if you're always going to use a brake, what's the point of riding fixed?
Fixed gear bikes are simple machines. you pedal forward to go forward, you pedal back/resist/or lock up the rear to slow down. I'm sure I'll get flamed, but i like skidding around turns and keeping my speed in check down a hill by locking up the rear from time to time. It can feel a bit like "controlling the chaos", but that's what I like about it. At first I was really sketchy on fixed gear bike, I could only skid by concentrating really hard and I felt wobbly and out of control. But over time, it's gotten a lot easier, i'm getting to where I can skid just as easily with either leg and I just feel like i have a lot more control over the bike if needed. kinda like driving a stickshift, at first you have to concentrate really hard on what gear you're going into, and not stalling, but over time it becomes second nature...