I think the big question here is who should then 'regulate' the marketplace of ideas? In a free speech society is this the government? Is it corporations?

In either case or a combination thereof the regulation will undoubtedly contain bias. Thus why free speech is supposed to be free speech.

In economics it is understood the only way to accomplish a true monopoly is through government regulation. If we allow government regulation of in the marketplace of ideas we run a very real risk of seeing monopolies of ideas.