There are a ton of very fine but not necessarily rare or collectible lugged steel road frames from the 60s-80s that make great fixed gear conversions. In fact, I think they're superior to the NJS-approved track bikes that the fad followers covet, if you're going to ride it on the road. The geometry is better suited for the road, the forks and bridges are drilled for brakes, they have waterbottle cage bosses and pump pegs, and room for fenders.

As to why you would want a fixed gear bike? They are simple, reliable, fun, and can make you a better rider.