In a distributed web you need seeds. Whether they are called "servers", "peers", "devices", or "clients" is dependent on implementation and semantics. For the purpose of my comments I chose to call dedicated seeds "servers", because it made sense to me.
And yeah, we can do that now! I've even used an old cell phone with a busted touchscreen as a low power syncthing device. Mostly it was meant to relay notes between my phone and laptop if one or the other was sleeping or dead. It worked great. Eventually, I stopped depending on it, because I have a headless machine running now (a "server") that does the same thing.
All I had to do to migrate was share my syncthing directories with the server. It was a breeze. I didn't have to worry about configuring addresses or anything.
Also, the server is useful as a relay, but if my phone and laptop are both on, say if I'm working at the library or something, they just communicate directly. So I don't depend on the server in the same way.
That's, flatly, a lie. There's a whole passage in the middle about how needing servers is a weakness of HTTP that this gets beyond.
Instead, we could put Raspberry Pis in our walls? We can do that now.