Any algorithm looking for the "best" result is inherently partial to something. Best result in terms of most recent, most local to you, most-likely-what-you-actually-want, I mean, the dimensions are endless.
The concept of "organic search results" is only possible if the algorithm were public, and that's just not a realistic expectation.
>A corporation inserting its own pages into organic results means it's not a search engine anymore. It's "a paid directory service augmented by a search engine".
I mean, Google doesn't have to pay themselves to promote their own pages. If you want to split the difference at "a search engine, part of a larger business whose results might show up preferentially in that search because why wouldn't they," that makes sense to me.
Of course any human-written algorithm will have bias. But it's a reasonable expectation (and the current norm) that every page faces the same bias.
I'm not sure where you're going with your last comment. If you've got evidence that Google is manually promoting its own pages within the search results (not ads) then please provide sources. This has never been proven and Google have consistently maintained they don't do it.
(I'm not a Google fan but I believe them in this case because of the anti-trust implications)
Google originally picked a bunch of sites and included there own and gave them a 10 page rank. That meant they automatically ranked higher for the same words/term because of a higher reputation score.
That's the user expectation.
A corporation inserting its own pages into organic results means it's not a search engine anymore. It's "a paid directory service augmented by a search engine".