So called "conservatives" were soooo close to being able to have this realization before they regained the power of the government, vested it all in a unitary execuking, and went back to seeing that extraconstitutional coercion as a feature (like many "progressives" had for ~10 years or so).
The reason I judge The Twitter Files as a rightist talking point is that it's trying to pigeonhole the motivation for censorship solely onto the government. If an argument is simply about the coercive power wielded by corporations and governments, you don't need a smoking gun of cooperation/direction to tie the two - seeing them as similar organizations with similar top-down motivations suffices. That evidence is only important if you're aiming for reform using the first amendment (an understandable desire, but the wrong tool for the job), or trying to absolve the corpos as mere victims of the de jure government (delusional).