Shipping the model with the browser is exactly the opposite of what you are claiming.
The alternative is sending the data to Google.
The alternative is sending the data to Google.
If the onboard LLM means no data sending and you get your own little service wholly subservient to you like a good little program. That's nice!
If the onboard LLM means better data filtering, possibly even exploration of the local system, to send information to Google while lessening their datacentre bills running LLM services. That seems a little underhanded to just bake into things without notification.
Pick your assumption, you get your outcome. What are your assumptions?
Knowing Google, the local model probably means even more data are sent to Google.