I think there's some opportunity, if this doesn't already exist, to make some decentralized (WebRTC, with centralized fallback) way of synchronizing localStorage across multiple devices with a pre-shared key. A drop-in script would add functionality to show and scan a QR code or enter a 12 word phrase. It could even be a userscript running without the web app developer's involvement at all. A lot of hoopla for a word game, but could be quite handy in more scenarios.
I've been wondering whether IPFS might be a good answer to that - there is this, which supposedly works in the browser. https://github.com/ipfs/js-ipfs
Dump webrtc metadata onto ipfs, give the user the hash back as a "document key" (and maybe a password that was used to encrypt the webrtc metadata) to share with other people; they paste in the key, enter password, and tada, you have a multi user application backed by localstorage.
Of course this wouldn't survive a user changing IP (and perhaps other network attributes) but that might be an OK feature.