I thought this exchange in the transcript of the Moody case was particularly telling (I’ve bolded the response that I think shows an interest in imposing an equality floor):

JUSTICE KAVANAUGH: Can I — can I ask you about a different precedent, about what we said in Buckley? And this picks up on the Chief Justice’s earlier comment about government intervention because of the power of the social media companies. And it seems like, in Buckley, in 1976, in a really important sentence in our First Amendment jurisprudence, we said that “the
concept that the government may restrict the speech of some elements of our society in order to enhance the relative voice of others is wholly foreign to the First Amendment.” And that seems to be what you responded with to the Chief Justice.

And then, in Tornillo, the Court went on at great length as well about the power of then newspapers, and the Court said they recognized the argument about vast changes that place in a few hands the power to inform the American people and shape public opinion and that that had led to abuses of bias and manipulation. The Court accepted all that but still said that wasn’t good enough to allow some kind of government-mandated fairness, right ofreply or anything. So how do you deal with those two principles?

MR. WHITAKER: Sure, JusticeKavanaugh. First of all, if — if you agree with me with our front-line position that what is being regulated here is conduct, not speech, I don’t think you get into interests and scrutiny and all that. I do think that the law advances the — the First Amendment interests that I mentioned, but I think the — the — the — that interest, the interest that our law is serving, if you did get to a point in the analysis that required consideration of those interests, our interests —

JUSTICE KAVANAUGH: Do you agree then, if speech is involved, that those cases mean that you lose?

MR. WHITAKER: No, I don’t agree with that, and — and the reason I don’t agree with that is because the interests that our law serve are — are legitimate, and it’s — it’s hard because different parts of the law serve different interests. But I think the one that — that sounds in the — in your concern that is most directly implicated would be the hosting requirement applicable to journalistic enterprises.

So one provision of the law says that the platforms cannot censor, shadow ban, or deplatform journalistic enterprises based on the content of their publication or broadcast. And that serves an interest very similar to the interest that this Court recognized as legitimate in Turner when Congress imposed on cable operators a must-carry obligation for broadcasters.

And — and just as a broadcaster –and what the Court said was there was not just a legitimate interest in promoting the free dissemination of ideas through broadcasting, but it was indeed a — a compelling interest, a highly compelling interest. And so I think the journalistic enterprise provision serves a — that very similar issue….

[20 pages later….]

JUSTICE KAVANAUGH: Well, in the Turner case, the intervention was, the Court emphasized, unrelated to the suppression of speech, the antitrust-type intervention there. So I’m not sure when it’s related to ensuring relative voices are balanced out or there’s fairness in the speech or balance in the speech, that that is covered by Turner. Do you agree with that?

MR. WHITAKER: No, I don’t agree withthat, Your Honor. Our — our — our interest and our law —

JUSTICE KAVANAUGH: What did Turner mean by “unrelated to” the suppression of speech?

MR. WHITAKER: Well, we don’t view our law as advancing interests that are related to the suppression of speech. We think that the interests, for example, in protecting journalistic enterprises from being censured, from — from MSNBC being censured because an Internet platform doesn’t like a broadcast it showed on its station the other day, that is just an interest in preventing from being silenced. **It’s not an equalizing interest. It’s giving them a chance.**

The idea of giving everyone a chance to speak on a social media platform is an equalizing interest.

(Note that although the transcript uses “censuring” here, I believe Whitaker said “censoring.”)