I had belt drives on three of my motorcycles (my current MC, a Moto Guzzi, has shaft drive). The belt drives were quiet, clean, and never needed maintenance. A rock embedded itself in one of the belts, but since it was in the middle, was no problem. That's what the tech said and he was right, for 20k miles, and beyond for the present owner.
A belt on a bicycle would last the life of the bike for 99.9% of us. I am looking for a new bike with belt and IGH, perhaps remembering the 3-speed IGH in my Schwinn from my youth. Heh, I would also like level ground, but Seattle isn't made that way.