In short, it is to prevent secession and civil wars, and to limit federal power over individuals.
In more depth, the U.S. is vastly more culturally diverse than most other nations. Its history of open immigration means it is now culturally a distorted, but still mostly recognizable, 1:20 model of the rest of the world.
If you ever want to visit India, China, Italy, Greece, Poland, Mexico, Sweden, and Germany in one day, just fly to Chicago and buy a CTA pass.
It is not a one-size-fits-all country. If the state is protecting a law that seems backward to you, it may be because they live on the other side of the looking glass from you. To them, your opinion is backward.
In Wisconsin, you can buy olives, gin, and vermouth in the same store, but only before 9 PM. In North Carolina, you have to buy the olives and vermouth in one store, and the gin from another. Why are the laws different? Because the people who live in those places, on average, prefer it that way.
State autonomy also allows for a limited sort of political experimentation. For instance, North Carolina can experiment with telling transgender people what bathrooms they must use, and Colorado can experiment with legal recreational marijuana. By observing the change in state economics, other states can respond more appropriately to the national zeitgeist. Federally, marijuana is still schedule I, and transgender people are not strongly protected against discrimination, but state autonomy has shown that the feds are wrong about weed, and that people prefer their identity to be something that is declared rather than imposed.
Why are the laws different? Because the people who live in those places, on average, prefer it that way.
I agree that there is value in trying a diversity of approaches, but I'm doubtful that a "will of the people" explanation can explain the state by state differences. Assume two groups of people, one from North Carolina and one from Wisconsin, but somehow we didn't know which group was from which state. In an attempt to determine this, we poll each group with a single written question about how best to regulate the sale of olives.
At what group size are we able to reliably identify which group is which? I'm doubtful that this is possible to do with greater than 90% accuracy at any group size less than the full population of each state. To the extent that it might be possible with lower accuracy, I'd guess it's based on the "status quo" rather than an actual "preference".
For many issues, I think it's likely that the initial decision is essentially random: one merchant convinces one legislator to propose a law. That legislator trades favors with other legislators to get the law passed. With the patina of time, the arbitrary self-interested law becomes associated with prosperity, "strong moral values", and evidence that Our Great State is still in the favor of God.
ps. I'd been meaning to ask you why your moniker is "logfromblammo", but a web search delightfully answered this for me: https://www.youtube.com/watch?v=2C7mNr5WMjA. I'm embarrassed to say that I previously was ignorant of this piece of retail history. Thank you.
In a lot of cases though, states themselves are too diverse and unwieldy to govern as a unitary entity. Texas and Massachusetts may have their differences, but Houston and Austin have much more in common with Boston than with a small town in the Piney Woods. Why shouldn't Houston be free to experiment with legalized marijuana just because the state government won't go along? By that same logic, it is state power over local governments and individuals that needs to be limited and municipal rights that need to be protected.
In my opinion, it is actually in my best interests for any government claiming jurisdiction over my person to have flawed mechanisms for enforcing its will upon me and extracting property from me. I consider that to be an adequate balancing factor for any inefficiencies it may also have in providing services or managing the commons.
Other people may prioritize such things differently.
I'm not arguing against the idea that government needs coercive powers. I'm arguing against the idea that states are the optimal organizational level to have unitary and sovereign governments.