I don't see why the search engine would work differently or be any less popular if Google used its algorithms to determine intent (that's Google's whole thing)

I don't see why the search engine would work differently or be any less popular if Google used its algorithms to determine intent (that's Google's whole thing) and then automatically (or via human moderation) prevent companies from showing ads when there is clear intent to find another company's brand. Google would be somewhat less profitable, perhaps, but the search product would still work fine (arguably even better) for the people searching.