Achieving consensus using browsers as nodes is unpractical for many reasons. Firstly, there are hard limits on localStorage, then there is the issue that nodes go offline really often (whenever someone closes their browser/tab) and therefore it's highly volatile - You would have to replicate data across nodes like crazy to reduce the odds of data loss (the bandwidth use would be massive with loads of duplicate data all over the place). Plus you still need a server to do the signaling to coordinate consensus across all the nodes. Also, there are security implications when storing data inside other peoples' browsers (though this isn't relevant in this specific case).

There has been some hype around using WebRTC for storing data only on the client-side using consensus algorithms like RAFT, but given the constraints which most browsers have and the massive amount of complexity required to get this working, it's really not worthwhile.

I don't think these browser constraints will be lifted anytime soon - There are some very good reasons for having them in the first place - For one, most people don't want their computers' CPU, memory and their internet bandwidth to be used up to process other people's stuff.