The problem is you can't break up Google. I mean you could, and it might work. For maybe like 10 years. But search is so huge and brings in so much fucking money, Google would basically grow into 'Google' again. Its a literal cancer, you can cut away the tumor but it will just keep growing back.
Thing is, Google is so ubiquitious and nobody has made a search algorithm that's even come close. Bing is a joke and DuckDuckGo, while laudable, is still not all there. Google does everything it can to monopolize search and keep it on lock. The only way Google gets brought down is if it infects the search division with SJWs, ideals over profit and hiring quotas so that Google's corporate culture becomes so fucking terrible that it makes every competent engineer flee the company. At this point, the only thing that can bring Google down is Google itself.