What would happen if the national law were not supreme?

If we did not have the protection of Constitutional Rights there would be regional pockets of intolerance where the prevailing majorities would pass laws that violate the rights of the minorities. There would be no balance. It is part of human nature for the powerful to take advantage, and control, of the less powerful in order to further their own desires and self interests. If that were to happen we would descend into a quagmire of hodge-podge laws and we would lose the stability and intelligence of the national framework of equality we now experience.