Even here with HN crowd: it's not an index, it's not stored on a server, and it's not typical send-securely encryption (not PK or symmetric "encrypted in transit", but homomorphic "encrypted processing"). Users will think that's all gibberish (ask a user if they want to send an index or vector representation? no clue).
Sure, you can ask users "do you want to use this". But why do we ask that? Historically it's user consent (knowingly opting in), and legal requirements around privacy. We don't have that pop up on any random new feature, it's gated to ones with some risk. There are questions to ask: does this technical method have any privacy risk? Can the user make informed consent? Again: I'm not pitching we ditch opt-in (I really don't have a fix in mind), but I feel like we're defaulting too quickly to "old tools for new problems". The old way is services=collection=consent. These are new privacy technologies which use a service, but the privacy is applied locally before leaving your device, and you don't need to trust the service (if you trust the DP/HE research).
End of the day: I'd really like to see more systems like this. I think there were technically flawed statements in the original blog article under discussion. I think new design methods might be needed when new technologies come into play. I don't have any magic answers.