https://www.youtube.com/watch?v=x79l7UO_qww
Caveat: The bike used is an e-bike with a powered wheel. The pedals have very little load requirements and no long-term or load testing is shown. As one of the most hardcore roadies you'll ever interact with, personally, I believe this would not last more than a week if it could survive a single ride on a traditional bike and someone like myself based on my first impression of the design. Still, the idea is impressive to me. In practice, a robust enough design will likely outweigh a chain drive by an order of magnitude. The reason the chain and cog transmission is standard is because of the balance of weight to durability. Every single gram matters on a bicycle far more than may be apparent at first.
Weight is really the only reason, but even then I think that's self-defeating on a bicycle.
Believe it or not, a chain and sprocket drive is actually the most efficient method in terms of energy transmission losses. And when it's you physically pedaling your bicycle, that's kind of important. Turning any significant fraction of your pedaling input into heat rather than forward locomotion is kind of a raw deal, which is why even fancy high end bicycles are still chain driven even to this day. A chain drive loses 1-4% of energy in the driveline whereas as comparable belt drive is more in the order of 9-15%.
If you compare apples to apples there's barely even a weight savings. Belt drives are either single speed or hub drive which can work with chains just fine. Once you add tensioner circuitry it's basically a push. The only kind of advantage is that they don't need lubrication and are quieter.
Exactly, which is why I was trying to think of any actual reasons I might want a belt, except style.