I recently finished Tim Wu's "The Master Switch", which is a history about the early radio/telephone/television/film industries, consolidation in those industries, and the effects on free speech.
One of my favorite examples from the book is the story about Hollywood and the Production Code in the 1930s. This was a voluntary code that the major studios obeyed for their own commercial interests (they wanted to avoid boycotts by groups like the National Legion of Decency). Because the film industry was centralized (with a small number of companies controlling all film production and distribution and most of the national theaters), this private decision by a handful of companies led to effective censorship in nearly all film in the US for ~20-30 years, all without any government action whatsoever.
I think we're in the same boat here with Google and other major internet infrastructure providers. Because a huge amount of power over the internet is concentrated in the hands of a few companies, those companies need to be very careful about the way they handle censorship.
"In an information industry the cost of monopoly must not be measured in dollars alone, but also in its effect on the economy of ideas and images, the restraint of which can ultimately amount to censorship."
"The story of Daniel Lord and the Legion of Decency goes to a central contention of this book: in the United States, it is industrial structure that determines the limits of free speech."
https://en.wikipedia.org/wiki/Motion_Picture_Production_Code