For basically every progressive ideal, none of it is pioneered by the federal government.
Gay marriage, legalization of drugs, continuing environmental standards, renewable energy, more sustainable living, and I'm sure many more, are all things that various states pass laws surrounding before the federal government steps in.
Think about how european citizens feel about the E.U. Today it would be crazy to ask a country like Germany to just roll over to the demands of the E.U. But I'm sure 200 years from now, if the E.U. is still around, that line will be a lot more blurry. This is essentially the position america is in.
Fun fact: At one point U.S. states each had their own currencies
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.
Other people may prioritize such things differently.
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.
Should Mississippi rule over California? Should New York rule over Texas? Most will reject at least one of these propositions. Thus, the United States are a system of divided powers.
It is perhaps instructive to note that the US is the 4th largest country by landmass. Canada, 2nd largest, is also a federation. (The other two are Russia and China)