If someone were to invent a new method for information retrieval superior to a search engine they could thrive.
As for proper monopolies it's usually the power/water utilities, although I think that the breakup of at&t back in the day was ill advised because their monopoly sustained bell labs, possibly the greatest innovation hub ever, that being one example of these populist antitrust notions backfiring.
Search ads isn't the only way to reach people and it's not an impediment for new entrants as shown by Amazon's ad business.
As for the general matter, google has the right to publish and design their website however they see fit, it's a no brainer, the only reason this question keeps popping up is that google has very powerful enemies in basically all news and publishing companies (they blame it for their dwindling ad revenue), not to mention the oracles and yelps of the world and all of them are piggybacking on the infrastructure laid down by microsoft at the time.
There is no monopoly when your stuff is free, has virtually zero replacement cost and no lock-in.
The "google is a monopoly" trope was introduced and cultivated by Steve Ballmer's Microsoft and it's being constantly adopted and revised by anyone with an axe to grind.
"Mississippi, Democratic Attorney General Jim Hood has sued the company for its handling of students’ data. For years, the two sides have warred repeatedly, with Google at one point suggesting that the Democratic attorney general had wrongly targeted the company with the aid of its foes in the movie industry."
I think that a system that allows people who have produced (Page, Rubin) to be subject to to the tantrums (legal and otherwise) of those who didn't is a broken system.
As for proper monopolies it's usually the power/water utilities, although I think that the breakup of at&t back in the day was ill advised because their monopoly sustained bell labs, possibly the greatest innovation hub ever, that being one example of these populist antitrust notions backfiring.