I agree that Congress could write a law that allows them to compel speech, and I agree that it might eventually be found constitutional. They didn't write that law, though, and speech that is both compelled and false is a different thing under the law than shutting up.

The government can't just order you to do whatever they like. That's what rule of law means. Nobody is obliged to obey someone's interpretation of the spirit of some law, just the letter.