These are basically timing belts for cars. Inside the belt are usually metal or aramid fibers that prevent any elongation of the tooth pitch. A lot of the automotive aftermarket principals of a timing chain versus a timing belt drive apply exactly the same here. The belt lasts longer and operates dry with more accuracy over time.

No, some 1200cc motorcycles use them.

Belts are a standard system for bikes already. Its the printed parts that are scary.

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%.

The positives of a belt drive are maintenance, and that it stays clean so they are most popular with commuters that do not want a dirty pants leg or newbie chain tat. They are only common on heavier bikes like short haul commuters in general and require a "broken frame" that is designed for them in the first place. The lack of transmission gearing means you need to either know exactly what gear ratio you need and deal with only having one speed or you need an internally geared hub. All internally geared hubs have monstrous weight to add. So in practice, you do not find many of these on the market. Even with an e-bike, you still need a geared transmission unless you have throttle control without pedaling.

On the other hand, for a hipster roadie, a fixie with a belt drive is some serious cred. Especially if they can dish it at the local group ride against people on flagship bikes.