I assume you're referring to the 1A rights of the corporation, e.g. Twitter's right to decline to publish content it disagrees with. I agree with you there. It's a complex problem. My complaint is more with the argument that only the government can restrict free speech. It's a lazy argument because the reality is far more nuanced than that. For example, consider the fact that AT&T doesn't have the right to drop your phone calls when you start talking about Verizon to the person on the other end of the line.
It's totally fair to talk about the "spirit" of the constitution -- that's why we have the Supreme Court in the first place, to interpret the constitution when its words are not clear. I would also note that the Declaration of Independence doesn't mention any self-evident truth about corporations, but it does describe the rights of the people, and government's role in preserving them. If corporations appear to interfere with those inalienable rights, it's not unreasonable for the government to step in to preserve them.