I was thinking exactly the same thing. If there is no severability clause how can it stay in effect?
The usage of a severability clause in writing legislation is merely something Congress does for their own purposes and to hem in their internal opposition if a law has to be fixed after court action.
A court is not bound by that in making their ruling and in this past century has held that the body of the legislation can stand if there is a part that is unconstitutional. They take the postition that Congress makes the laws and congress can fix those items struck down.