This seems like it ignores "despite an ever larger portion of public speech being conducted through corporate platforms."
Compelled speech is (rightly) illegal in pretty much all cases, and while "both or neither" is not quite the same as directly compelling a specific statement, it's still not a free-speech-respecting stance. The thorny question is how to handle public speech conducted through private platforms - for instance the suit over whether President Trump can block people on Twitter. Twitter is obviously a private platform, but it's being used by a public figure to make policy announcements, and blocking restricts the ability of certain people to see and respond to those announcements.
"Public forum" doctrine is controversial, but it's far from new. More broadly, it's the First Amendment application of a larger question: how far can the government go in using private intermediaries to bypass constitutional protections? On the Fourth, police are allowed to use private tips with origins that would be "unreasonable search", but can't proactively request or pay for such searches. On the Fifth, a non-government party might prompt admissible hearsay by means not available to the police, but that doesn't free the police to hand off interrogations to private parties.
That sort of constitutionality-laundering is an increasingly pressing issue, everywhere from warrantless lookups of mobile phone locations to public speech conducted on Twitter. And this is quite clearly the claim laid out in the article (though it's not a US case): that airports are so closely linked to the government that their ability to control speech (especially speech related to government behavior in airports) is restricted. It's a matter open to dispute, but it's very much not as simple as compelling speech from a private party.
I think it's, for example, eminently possible to reconcile Twitter's right not to be obligated to carry "hate speech" (aside: please don't derail this discussion with an unnecessary diversion into whether that's a thing, or where its boundaries are; this is meta-level) with the President's not being able to block people.
If he's using the platform to conduct "official" business (which, IMO, he is), blocking is pretty obviously not kosher. That's an utterly different case than whether they should have to promulgate Joe Bigot's shitty opinions. We already have structurally similar legal doctrines in place in the case of libel against public figures, for example.
Looking for blanket solutions is the wrong idea, out the gate, however much more difficult and nuanced that will ultimately make handling the thorniness of the issue, taken large, and I think you actually already appreciate that, with your takes on the 4th and 5th Amendment questions.
Twitter is very much not obligated to pass along any random person's terrible views (and thanks for the disclaimer; no interest in seeing that argument again). If Trump decides to conduct official business there, they aren't quite facing compelled speech because they can (in theory) ban him; the outcome we'd hopefully get is that his official speech is restricted, but Twitter is free to host him or not.
I suppose at this point the only question is whether a government-proxy rationale applies to airports in this specific case, since I definitely agree that Kayak or Travelocity couldn't be required to accept these ads on their site.
Compelled speech is (rightly) illegal in pretty much all cases, and while "both or neither" is not quite the same as directly compelling a specific statement, it's still not a free-speech-respecting stance. The thorny question is how to handle public speech conducted through private platforms - for instance the suit over whether President Trump can block people on Twitter. Twitter is obviously a private platform, but it's being used by a public figure to make policy announcements, and blocking restricts the ability of certain people to see and respond to those announcements.
"Public forum" doctrine is controversial, but it's far from new. More broadly, it's the First Amendment application of a larger question: how far can the government go in using private intermediaries to bypass constitutional protections? On the Fourth, police are allowed to use private tips with origins that would be "unreasonable search", but can't proactively request or pay for such searches. On the Fifth, a non-government party might prompt admissible hearsay by means not available to the police, but that doesn't free the police to hand off interrogations to private parties.
That sort of constitutionality-laundering is an increasingly pressing issue, everywhere from warrantless lookups of mobile phone locations to public speech conducted on Twitter. And this is quite clearly the claim laid out in the article (though it's not a US case): that airports are so closely linked to the government that their ability to control speech (especially speech related to government behavior in airports) is restricted. It's a matter open to dispute, but it's very much not as simple as compelling speech from a private party.