There's a very strong financial incentive for ad-powered search engines to keep SEO spam out of search results, because that makes advertisers more willing to pay for search placement. A publicly run search engine would not have those incentives and would be at if anything graver risk of a "tragedy of the commons" type scenario where the engine is overtaken with spam.
Yes, there are perverse incentives to populate search engine results with paid placements, but the best corrective force I can think of is having more competition in the search space. As long as people are willing to try other search engines (spoiler: for the most part, they are currently not), this creates a strong incentive to ensure that paid placements that harm the search experience are kept to a minimum.
...and I think the concerns about profitability of the LLM space is completely missing the larger agenda. Even if public use of OpenAI and its competitors NEVER TURNS A PROFIT, there is tremendous economic opportunity that investors expect to realize from a company with intelligent/powerful LLMs. That is why they are pumping so much money into these companies.