This seems significantly laborious. Not sure that the utility of this kind of network recommendation scales to incentivise participation beyond a few people. i.e.: We already have user groups on sites like reddit, FB etc, where experts or enthusiasts answer questions when they feel like it. But this is a slow process that relies on a group that contains enough distributed knowledge, but isn't overwhelmed with inquiries. As a counter example, the /r/BuildaPC subreddit long ago exceeded the size where it could answer a significant proportion of build questions, and most remain unanswered despite significant community engagement.
Not convinced any kind of formalised 'question answering network' could replace search. It would be both slow, and require an enormous asymmetric investment of time, for a diffuse and unspecified reward.
Suppose you like fountain pens, and you recommend certain ones. One of your friend looks for fountain pens that their friends recommend and finds the ones you like.
That is just one example of things that don't require explicit questions.
Another one might be you have searched for books or other things and then they follow the same "path". So long as you have similar interests it might work.
People haven't solved this issue, but there is a lot of research out there on networks of connections potentially replacing certain kinds of search.
Not convinced any kind of formalised 'question answering network' could replace search. It would be both slow, and require an enormous asymmetric investment of time, for a diffuse and unspecified reward.