I would have interpreted it in quite the opposite manner. States (within a single country) having different laws is nuts to me.
A common legal system has little to do with different cultures within the same country. If you extrapolate in the British case, you'd have had sharia law decades ago in some towns and the certitude of that increasing in proportion to birth rates. I wonder what the good folks of France would think...
Either you are a country of equal rights and a common legal system or you are a loose federation wide open to departures. That's part of the cause of Scottish Nationalism: it has a lot of its own, different laws, and that tempts further distancings to seem sensible courses to some.
Not all countries want to be that closely tied together; fears of a federal Europe scare some countries out of their pants, and in that particular case, I agree that it would be an ill-matched bundle of tribes that could never hold that close a relationship for all sorts of historical and ethnic reasons.
Rob, As Slobodan said, we're a federation. The US was founded when 13 sovereign states decided to federate. But the founders were terrified by royals like your George III and centralized governments of history. They wanted a very weak central government. So they gave enumerated powers to the central government. Things like printing money, making treaties with other countries, manning an army and going to war, a post office, the right to regulate interstate commerce. All other power would flow to each of the individual states and their people who would decide how they want to live. So some states have capital punishment and some don't, some states have income taxes and others don't, some states have a maximum speed limit of 75, other may have 65mph. Each state has its own constitution, legislature, rules, police, etc. The US Constitution also has its Bill of Rights. Things like freedom of speech, the press, religion, etc. that no state law can abrogate. So the people are protected against oppressive state government as well.
Regarding how we know we're Americans and of one tribe if we have 50 different states. Great question. I'm reminded that for 70 years or so after the USA was founded, people would say the plural "Well, the United States
are ........" The Civil War changed that. Afterwards, people began saying the singular, "Well, the United States
is....."