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.