I think maybe my lack of knowledge on syncthing and my bad explanation of this “hosting” feature has made my post (and title) somewhat misleading.
The effects of the above described feature would probably be the same as hosting files on a public web server with authorization combined with some mechanism for handling changing IP addresses of hosts. But imo syncthing could probably do this in a much more simple, out of the box manner compared to setting up a web server, then setting up authorization (maybe using certificates), then handling changing IP addresses. With syncthing it could be as simple as install syncthing, add devices, share folder and then you could start sending local http request which are actually serving non-local/shared data.
Hope this makes more sense. And fair enough if this is still not something you see syncthing solving. For me the simplicity of using syncthing is really one of the great benefits and a “hosting” feature like this seems like a pretty good opportunity to increase usage of syncthing. But of course I could be wrong