That's something many humans already suffer from, due to social media platforms creating large echo chambers.
I think there's enough human-generated content that LLMs won't suffer from that. If they did, you could always manually filter what they train from... only data from websites with trustworthy timestamps pre-2020, for instance, or content after that which might be partially AI generated but still has strong human filtering, like wikipedia and arxiv and scientific papers in general.
Just no. It would have to take more than that to challenge Google's business model.
This current AI hype around LLMs and chatbots is the start of a hype cycle similar to what happened to Clubhouse.
Also, for now these services are spending a lot of money to capture the market, but sooner or later they'll monetize by biasing results towards their paid advertisers.
The end user isn't the customer, advertisers are.
Also, I believe google willingly puts blog posts with ads on top, rather than the original documentation/maling list discussion because those usually have no ads.