There are good reasons for a bike with only one gear. If the bike encounters few hills, low winds and moves at a moderate pace one gear could be all that’s needed. Removing gears, levers, cables, lowers weight. What’s not on the bike will never need adjustment, lubrication, maintenance or replacement (and won’t leave stains).
Racers train on one-gear bikes off-season because you can’t cheat going uphill or up wind by down-shifting. Fixies can’t ever stop pedaling, even downhill spinning is required.
There’s a ‘Zen’ of one-gear bikes too, especially fixies. You hear only the wind and the tires on the pavement, not freewheels and off-center chains. You’re in direct control of the bike at all times. Want to speed up? Pedal faster. Want to slow down? Pedal slower.
You can hover, push back to slow down, or with fixies skid to a stop, or ride backward! Going up a hill? Pedal harder or stand up and pump, or get off and walk, no shame in that.
Fixie riders can’t coast or stand up to rest their butts, a point for the singlespeed. Singlespeeders can coast through turns at high angles safely and coast joyously downhill, standing up just for the hell of it, while fellow fixiest must spin like mad downhill and push backward on the pedals to slow down, a new strain said to cause knee and muscle soreness.
One-gear bikes are slower than geared ones; fixies are harder to mount and dismount and demand more attention on turns to prevent deadly pedal strike. 
But any bike can kill you in a second. So wear a helmet and drive defensively.
Vintage steel bikes are durable and strong, have a springy ride, and use long ‘horizontal dropouts’, making adjusting the chain and rear wheel easier.
I find the colorful, detailed and beautiful head-badges attractive and the original paint, decals and stickers romantic. They don’t build them that way any more and I’d hate to see them vanish.
