First, let me clear up a few things. I do not suggest that Google should be singled out because they are Google, but because of their dominant position in the market. This is what anti-trust laws were designed to do: to prevent abuse of the dominant player or players in a specific market. The potential from abuse comes from the fact that they are dominant and ostensibly unassailable in their market, and that their actions may indeed influence the market directly or indirectly; even if such actions are perfectly acceptable for any other player without as much influence.
Second, regarding the definition of a "search engine," I base my statement on what a traditionally search engine was understood to be. You are right, this definition harks back to the days of yore when Altavista roamed the plains with the dinosaurs.
That said, I agree with you that search engines have morphed into something different, and arguably more useful. This is precisely my point, that although they changed their business models and service focus, Google and their ilk still want to operate in relative obscurity as if they were mere "old school" search engines.
On the one hand, Google claims that they are mere aggregators and conduits to content, and that they do not curate nor create such content, therefore they are not liable for its semantic accuracy, topics, or expressions. On the other hand, they keep adding services that interact directly with the end-user, composed of information that, although may have been gathered from external sources, was actually edited* and filtered subjectively by them.
So, which is it? Is the resulting content theirs or not? Is it curated or merely aggregated? Is it edited? Obviously a lot of people, like you, expect Google to "give them what they want" directly. However, you must admit that this is mostly a recent development in the mainstream; traditionally, Google was expected not to answer questions but to return "stuff from the intarwebz."
Regardless of this, what about advertisers position? Should they expect that they are bidding for ranking based on the unbiased results, or are they actually competing directly with Google? This is important, because I should not expect them to continue paying Google for the exposure, if such exposure is always guaranteed to go first to Google.
Imagine if I went to an independent car dealer and asked them to put a poster for my specialty car on their window, and that I were bidding for the most prominent window placement against other small car manufacturers. Would my surprised be justified if I ever discovered that the "independent" car dealer had a direct contract with Toyota and will always give the most prominent window position to them, regardless of how much money me and the others were paying for the same position? Would it be any more fair if the car dealer responded with something like "it's OK, we can't tell you how we pick the winner, but I can promise you it's fair. Even if it looks like Toyota always shows up."
Ultimately, all that I am suggesting is more transparency on the part of Google (and other search engines too). Such transparency may indeed prove that the model of "auctioning auctioneer" or "competing partner" is as an unsustainable one, and as absurd an oxymoron as it sounds.
* Note that here "edited" is used in its standard definition of "to supervise or direct the preparation of content; to collect, prepare, and arrange materials for publication.