I've always liked the idea of this. It's not just for single speed. Should work well with a Sturmey or other hub gear. I would imagine it would be a lot quieter than a chain, would be lighter and doesn't need oiled, therefore less messy. This would make it excellent for folding bikes. Anytime I put my folding Raleigh into the car, I usually seem to get oil of the chain all over my clothes. The Strida has a belt drive, presumeably for this reason and rides as well as can be expected given the design of the bike.
Anyone who doubts the strength of a belt look at the stresses and strains the cam belt on a high reving engine takes for maybe 50,000 plus miles.