I really appreciate your approach to this argument. You really cut through any strawman fallacies by pointing out that there's a debate along a spectrum about what protecting free speech entails, but that the President needs to have limitations in his power over private companies. I think this final point is not debatable in a legal context; he does not legally have that power.
Either the president does not know the constitutional limits on his power, or he knows them but still thinks it's a good idea to claim power that he does not have. I'm not sure which is worse.