That would be a paid service that the majority of people would not be okay with, and even if google search did an enshittification pass trying to create a crowd that would. Users would still jump ship to the next search that is still provided for free.
How is Chrome going to make money as a standalone company? I have no idea, but it probably aligns with your guess
Boeing used to own an oil company, engine manufacturer, airline, and airplane manufacturing. The US government broke them up because nobody can compete with that vertical integration.
This is a common issue addressed by strong anti-trust regulations.
If Google (or any online business) is prevented from owning a web browser then the browsers compete on merit. Consumers choose what is actually good for them.
Google has no incentive to make a good browser for consumers. They only have incentive to make one that is good enough for consumers to behave in Google’s interest. And if nobody can compete then that bar is low. Consumers don’t know what they are missing. Nobody does because we haven’t had a competitive browser market in close to three decades.
I think your example is completely wrong. Chrome has no source of funding. If separated from Google, they will have a massively magnified incentive to cater to the whims of advertisers because they would be completely subservient to them for funding.
My understanding is that Chrome provides value to Google through intangible means like brand association and thus Chrome does not have to 100% justify its existence by enabling ads for Google, meaning that it has some funding to just be a good browser for consumers.