What's a fixed gear bike? Why, a bike with only one gear, so that you go slower by pedaling slower. And it has no brakes.
In other words, exactly like the purple unicorn-adorned, handbar pom-pommed First Bike my sister and I had as kids. Oh wait no... you could backpedal for some braking, I think. A ten speed was something spoken of in hushed and reverent tones, because Really Big Kids - TEENAGERS - had them.
I don't... I mean, if you're a messenger in NYC, sure. It's mostly flat, you're pedaling all-out and dodging and weaving - changing gears is a distraction you don't need. If you live or bike somewhere flat, or if you enjoy the challenge of getting from A to B without the "cheat" of mechanical advantage... more power to you.
But if you're going to pay more for a bike that does less because that's somehow ironic? That word... I do not think it means what you think it means.