It's worth noting that the initial proposal for WWW (https://www.w3.org/History/1989/proposal.html) was actually for a distributed/decentralized network, requiring no central authority/control:
> CERN Requirements - Non-Centralisation - Information systems start small and grow. They also start isolated and then merge. A new system must allow existing systems to be linked together without requiring any central control or coordination.
As the web grew, this obviously became less and less true. But I don't think there is anything in particular in the initial ideas for WWW that locks it into a client/server model, although that's what naturally happened.
> Non-Centralisation
I imagine this term was used because it was before everything got centralized, so there was no need to "de-"centralize yet.
> client/server model
The original design of the WorldWideWeb application was a web browser and editor, which I think implies that anyone using it could run a server as easily as browsing other people's servers.
Edit: Not totally sure, but it does seem there was an HTTP server bundled with the browser/editor.
How to make a WWW server (1992) - https://www.w3.org/History/19921103-hypertext/hypertext/WWW/...
WWW Daemon user guide - https://www.w3.org/History/19921103-hypertext/hypertext/WWW/...