Give it X months (or years??) and people will realize this is actually a privacy/data autonomy issue.
It's just dominated right now by the anti-AI/anti-technology sentiment in the west. That will gradually go away as more people use AI and robotics and realize how wrong they were about it.
Nothing in this proposal claims it has to be a local AI. That just happens to be the implementation by Chrome and Edge (for now at least, I'd imagine Google will eventually start moving this API towards hosted Gemini).
I will use WebLLM if I want something like this (with local AI guaranteed).