These engineers are /not/ the engineers that are in charge of designing or running the systems that sell ads. In fact, those are two completely different divisions of the company. (If you would like to learn more about how Google works from the inside, I suggest reading Steven Levy's book "In the Plex")
Just because you do not pay for something does not mean it is not a product. If search was not good, people would go to a competitor. This is how Google got to where it is today, and bing.com is just a click away. This thread is about the quality of Google search results, and your argument is that Google does not care about the quality of your search results because they allow you to use it free of charge by inserting labeled advertisements.
To me, this is not a logical argument -- your emotions and sense of being wronged have taken over.
So, from the perspective of a business analyst, you are saying that Google has no incentive to ensure the quality of their search results because they don't receive any additional money from the people who use it?
That sounds like very short-term thinking to me, and Google is a famously long-term thinking company.
OT your line of reasoning reminds me of Excite when they were considering using Google's results. "[Google] was too good. If Excite were to host a search engine that instantly gave people information they sought, [Excite's CEO] explained, the users would leave the site instantly." [1]
[1] http://cdixon.org/2011/05/16/accurate-contrarian-theories/
Look, I'm not saying this is good or bad. But it is what it is.
You don't pay them directly. Yes, they get paid based on your repeat usage, but they get paid by advertisers.
Your instinctual reaction to frame this in the context of a market is faulty. ALL of the major search players operate under the conceptual mode of users as product, advertisers as customers. The same is true with other media companies (TV, newspaper, etc). That seems to be the only model the market will currently bear, as the existence of media giants is predicated on their ability to accelerate consumption