If you google gates belt drive snapped you‘ll find plenty of anecdata of belts lasting only a couple thousand kilometers (and others who ride them for tens of thousands of kilometers with no issues).
Here‘s a (German) Video from a guy with a severely damaged (but still rideable) belt after 4500 km:
Another disadvantage is repairability. If your chain snaps you can fix it with a quick link or a pin and a little multitool with chain tool functionality. If your belt snaps you‘re screwed, unless you carry a spare belt everywhere.
Here‘s a (German) Video from a guy with a severely damaged (but still rideable) belt after 4500 km:
https://m.youtube.com/watch?v=n16gN7RDWEY
In the comments you‘ll find people whose belts snapped at 1050 km, at 1000 km and one at less than 2000 km.
I don‘t know how likely this is, it might be quite rare. But since it‘s non-repairable it‘d make me uneasy on longer bike rides.