Marriage is a reality. You might as well ask states to eliminate the recognition of gravity in fall lawsuits.
The recognition by states isn’t the problem - it hasn’t been a problem for the vast majority of Western Civilization’s existence. The problem is the rise of the Left.
You have an entire subset of the legal profession -- namely, divorce lawyers -- who make careers dealing with the countless cases where one person can break a legally binding marriage without the consent of the other. The work order you sign with a plumber to fix your toilet is more legally binding than your marriage, under the laws of every state in the U.S. And this was the disastrous state of affairs BEFORE the Obergefell decision.