I think a social network is not necessarily a timeline-based product, but an LLM-native/enabled group chat can probably be a very interesting product. Remember, ChatGPT itself is already a chat.
Extend ChatGPT to allow multiple people / friends to interact with the bot and each other. Would be interesting UX challenge if they're able to pull it off. I frequently share chats from other platforms, but typically those platforms don't allow actual collaboration and instead clone the chat for the people I shared.
Would love an alpha tester or two if anyone wants to test it.
My email/twitter is in my profile, shoot me a message and I will be in touch.
For a moment I had a funnier mental image of a chat app with an input field that treats every input as a prompt, and everyone's chatting through the veil of an LLM verbosity filter.
There might be something chat RPG-like there worth trying though ...