If there was a company providing Syncthing-as-a-service I would very much sign up. I want the power of Syncthing (or similar) without the hassle of running a server myself.
A syncthing server is used for discovery only, which is a free service.
I use my NAS for this, that way I don't need to keep my desktop turned on for my laptop to sync to it.
That is, you can’t just point syncthing to any old sftp endpoint…
I think your parent means “the commercial endpoint” when he says “server” …
Every peer needs to have syncthing installed, yes. This is how syncthing works. It's P2P (though there is the public relay servers for NATed peers).
Even if you ran your own relay network, every peer would need Syncthing installed.
What some users might want is an always-on node, so that device A could push to that always-on node and then device B could later download it without requiring device A and device B to be online at the same time, but what that node is, is really just a device C that's always on.
I think you're picturing Syncthing as being like a centralised file host that offers a client to sync to/from it, or maybe like something like Borg or restic. It's not that, there's no master node or central repo or anything.
I use this feature with a friend of mine. We both have NAS', and we both have each other's NAS as an untrusted SyncThing device. (It's also pretty trivial to run a Linode/DigitalOcean low end VPS as an untrusted client. In fact if neither has a one-click install I'd be surprised.)