I've never had an iOS device, but does it even have a concept of a 'file system' exposed to the user? Presumably if the app existed, you could only view the files inside the 'syncthing' app, but other apps won't be able to read its data?
iOS does in-fact have a sort-of file system. It’s heavily tied to iCloud and I don’t think it’s really meant for sync thing style files. But it’s not like drop box is much different in this regard.