Software assistants summarising all my communications is intrusive, regardless of where the model runs.

How is it intrusive? Given charitable assumptions like granular permissions, silod app data only extracted through intents, and using only local compute?

I'm all for questioning Google on whether those assumptions will be true and no data leaves your phone, but I'm curious about the concept.

You're carrying an always on mic wired up to a closed source system with you everywhere you go already. It was already possible to stream or record everything anyway.