You'll find it hard to pin down what you mean by "everything" otherwise you wouldn't have said that. Nobody uses the internet for everything.
Local models are highly likely to dominate in the long run as "good enough" inevitably becomes trivially cheap. This is a very different pattern of incentives and adoption compared to the internet.
I think it's more similar to the advent of personal computers. They had a brief surge and then turned into something else (smartphones, cloud, etc.) for all but a few niche cases. AI is not changing the consumer landscape. It's getting absorbed into existing platforms where there's a clear use case and benefit. It's just another expected software feature. This is far from the first time people have rejected a "personal assistant" concept and they'll just keep rejecting it.
It seems fair to leave the definition of "everything" to a reasonable person's interpretation. It's obvious that the internet is beyond ubiquitous in modern life.
I agree that where models run will will change over time, probably they'll run everywhere, but it's still the same kind of AI we are talking about.
Smartphones are personal computers.