Many years ago the Supreme Court held that marriage only between men and women was legal and that sodomy was illegal. Yet courts later changed. And the court has ruled as I said above; anti-polygamy laws are constitutionally unenforceable for any purpose more than to allow the State to refuse to issue secular marriage licenses to someone already married.
In any event your acknowledgment of the point in your last paragraph makes the point moot since one can simply refrain from obtaining multiple state marriage licenses or otherwise representing himself to the government of being married more than once. He can simply stick to kiddushin.