Why do we need rights?
Holding elections on a regular basis is meaningless unless political and civil rights are protected for everyone, always. Without protected rights, you might not be allowed to vote or run for office if your opposition is in power. Even if you could do those things, elections would not be free and fair because incumbent officials could harass their opponents in all sorts of ways. They could make it illegal to criticize government officials, or assemble people together to hear a speech, thus making normal election campaigns impossible. They could harass the media or take it over, so the opposition has no voice. The government could search and confiscate opposition property for no reason at all. You could be wrongfully charged with a crime, and you might have an unfair trial that never gets fully resolved.
Once a party gets into power, it could use all these tools of repression to keep power forever. Instead, because of your protected rights, losing an election is not a disaster. Your party and your candidates can safely compete again and again.
Back when our Constitution was being debated, a group of the framers became very concerned that an overly powerful federal government could tyrannize the population. In particular, they wanted a weaker president and stronger states. They were known as the Anti-federalists. To deal with their fears, they insisted on a series of amendments to the Constitution before they would support its ratification. They insisted that it should be explicitly unconstitutional for the federal government to infringe upon basic political and civil rights. These amendments came to be known as the Bill of Rights.
The Constitution was amended several times after the civil war to extend those rights to all American citizens of age, notably people of color (13th, 14th and 15th amendments) and women (19th amendment). Those amendments did not, by themselves, automatically solve the problem. Jim Crow policies sponsored by state and local governments, and the acts of numerous private citizens, ensured that people of color would not be allowed to enjoy their political and civil rights. The situation did not change until decades of struggle by people of color and their allies finally mobilized a strong federal response in support of equal rights for all people.
In the end, arguments over the role of the federal and state governments in protecting rights are based on a false choice. The truth is that we have the power to elect or decline to reelect leaders in both levels of government. We can choose to respect the rights of all Americans and we use elections to require our federal and state governments to do the same. The principle of equal rights has long since spread around the world. It is something we should all proudly defend.