Judges in regular courts really don't like "one weird trick" style legal arguments. I'm guessing judges in secret national security courts like them even less. Hence the skepticism that, in this circumstance, they wouldn't just order the site to update their canary and threaten the operators with charges themselves if they refuse.
Judges in the United States also don't like compelling speech. So compelling a private entity to repeatedly update a warrant canary is unlikely to be legal.
I am not a lawyer, but my understanding is that this is the stated legal opinion of the lawyers at the EFF.
Indeed, the bar is (supposed to be) very high for this kind of thing. But at the same time, it feels like exactly the kind of "gotcha" that rarely flies, because the situation was so deliberately constructed. But without any (public?) litigation, it's anyone's guess what may happen.
