Perhaps we should come up with a system where people are free to use whatever search engine they like, and the government can't tell you what search engine to use, and the government can't tell the search engines what to publish. It would be so much better than the current system where we're legally required to use Google.
You forgot Amazon, but it sounds like we've moved the goalposts from free speech to fairness for advertisers now. That's an antitrust problem, not a free speech problem.