If the government can compel one kind of speech, it's not hard to compel others. They don't even have to make a a brand new rule for this. The companies have stated they use this technique to get around the gag order.

Judges aren't compilers who will faithfully follow all the rules as written down without deviation. They at specifically empowered to make decisions in light of new evidence, so why wouldn't they force companies to actively like if they are already adding exceptions to the first amendment?