"Daphne Keller, who studies these things over at Stanford Law School's Center for Internet and Society has both a larger paper and a shorter blog post discussing this, specifically in the context of serious concerns about how the Right To Be Forgotten (RTBF) under the GDPR will be implemented, and how it may stifle freedom of expression across Europe. Right now, of course, the RTBF applies to search results, but under the GDPR it may expand to much more, including things like Twitter and Facebook:
Applying RTBF to platforms like Facebook, Dailymotion, or Twitter would be a big deal for Internet users’ expression and information rights. RTBF in its current form under Google Spain only covers search engines, and only requires “de-listing” search results – meaning that users will not see certain webpage titles, snippets, and links when they search for a data subject by name. Regulators have said that the RTBF is reconcilable with information and expression rights precisely because information is only de-listed, and not removed from the source page. But if social media or other hosts had to honor RTBF requests, much of the information they erased would not merely be harder to find – it would be truly gone. For ephemeral expression like tweets or Facebook posts, that might mean the author’s only copy is erased. The same could happen to cloud computing users or bloggers like artist Dennis Cooper, who lost 14 years of creative output when Google abruptly terminated his Blogger account."