Yeah, riding a fixed gear on the street actually DOES make sense, though only in relatively flat areas in my opinion:
* the bike is mechanically simple, and thus cheap and reliable (no worries about derailers, shifters, freewheels, etc.)
* a fixed gear provides EXCELLENT traction feedback on slippery surfaces. I find that I cannot ride my thin-tire road bike on snow at all, and slick pavement is very tricky, but can handle them well with a fixie.
* in city traffic, you can speed up and slow down very smoothly just with your knees, so you're not always braking and then struggling to get up to speed again. And you can trackstand at stop signs and stoplights with just a bit of traffic.
* it's a lot of fun for many people!
* it's good for training to improve your cadence

So riding fixed on the street can actually be very practical I feel. So not having gears may be worth it. But not having a brake is very foolish.