The Democrats control the House, the Senate, and the White House. They could easily and quickly pass legislation authorizing the CDC to make such a mandate.
That is how the law works. A law is written, an action is taken, and a judge (should) look at the action and see if it is authorized by the law.
A judge (shouldn't) look at the action and decide if it is noble and good, and ignore if the action is legal.
This.
And not only does a law need to be passed, but regulations need to drafted and there needs to be negotiated rule making before implementation. I work for a federal agency and have attended “neg reg” sessions. It incorporates community and stakeholder feedback. It takes months. It’s a process and the CDC violated the administrative procedures act.