Can anyone provide one benefit to a fixed gear? I can't think of a single reason why someone would want to have the pedals locked to the back wheel.
For me - none. Fixed bikes were designed to be used on closed tracks, where you just sit on it & ride a few laps before stopping. In traffic they're super dangerous, since they don't brake that good, and are fatal to you're knees - that's why most of the hipsters ditched them. They're not as light as they seem (especially the cheap ones), and not much simpler than single speed freewheel bikes with or without a coaster brake hub.
Also, since the breaking power is worst than in normal bikes with brakes they were forbiden to ride in traffic in many countries of the EU (Including Poland - since our traffic rules state that bikes must have at least one working brake). I remember when the Policeman in Warsaw started noticing the difference between fixies & single speed bikes and people riding on them were given large tickets for riding bikes that were not suited to use in traffic. It even came to it that if you had a flip-flop rear hub the only way to avoid a ticket like that was to remove the fixed gear cog, so that you couldn't do a quick change & use the bike as a fixie.
There are still people who don't respect that law, and ride their fixies, but it lasts only for a season or two and they get back to "normal" bikes. (Mostly because of their knees failing)
There even was a Romet bicycle that was a factory fixie - The Romet Wicher.
It was basically a Romet Huragan frame with a special shortened fork & track steeringbar, but like the Jaguar Specjal racing bikes they were only selled to bicycle clubs, so right now they're very hard to find.