FWIW I've toured on both and singlespeed is harder on the legs over long distances than fixed gear. I ran brakes but from what I've seen that's common. Touring on a fixed gear without brakes is usually done on track bikes and is kinda a separate thing than regular touring.

Anway, I liked it because it was an easy/cheap way to get a very light bike and forced me to pare down to a minimal load. I was regularly riding fixed on the road and realized that if I didn't need a geared drivetrain for my road riding I didn't need one for touring. I like the style of riding, it's simple - you just pedal and go.