The question actually asked, "what legal theories would support or harm...", is somewhat unclear. But what the questioner seems to be asking is, basically, what would happen if you tried it?
The answer, it seems to me, is pretty straightforward. In the hypothetical case, you have been publishing a notice for years, saying "I have not been served with a subpoena." You then get served with a subpoena that includes a gag order. The gag order, presumably, includes wording prohibiting you from revealing the existence of the subpoena.
You then cease publication of the warrant canary. By doing so, you have revealed the existence of the subpoena, and you are in violation of the gag order. You will be subject to whatever penalties you would be subject to if you violated it in some other way; for example, by publishing a notice that said, "Hey! We got a subpoena! It's a secret!"
The distinction between revealing the existence of the subpoena by action, rather than by inaction, is a false one. It's exactly the kind of cutesy legal formality that non-lawyers love to rely on, but real judges ignore. If you tell someone: "Hey, you know John Smith's three sons, Joe, Ted, and Bill? Joe and Ted are good people; they have never molested any children. As for Bill--well, I don't have anything to say about Bill." If Bill is not a child molester, you have defamed him, and you are not going to convince a judge otherwise.
The EFF link you link to tries to claim it'll "work" because courts are reluctant to enforce speech. Even if that were true, that might mean your canary would be effective in the sense of giving the public notice of the subpoena. That doesn't mean you wouldn't be liable for giving the public notice. For example: I put up a billboard saying "Bill Smith is a pedophile." Even if the court can't force me to add the word "not", that doesn't mean the billboard isn't defamatory.
Realistically, though, courts compel speech all the time. Court-ordered apologies, disclosures, and notices are not unusual. And if ever a court would be inclined to compel speech, it would be in a situation like this one, where a company intentionally set out to get around a gag order with this kind of convoluted sea-lawyering.