Striking is not the same as speech. It goes far beyond. They can't stop teachers from protesting or speaking out. No law could do that. They can, however, immediately fire and replace anyone who refuses to work, absent strike protections. They can call in the Pinkertons to break picket lines absent strike protections.

It's not about expressing themselves. It's about collective bargaining with the threat of the employer fully losing access to the labor if they refuse.

And the NLRA specifically does not cover public sector employees, so they can absolutely ban teachers from striking. They shouldn't, but they certainly could.