In most countries, even with highly autonomous provinces, the central government can simply pass a law to change their status at will.
In the U.S., it cannot. The U.S. federal government only has the right to legislate in a small, whitelisted set of areas and does not have the right to change anything about the States' status or individual State laws beyond that.
In Canada, the constitution enumerates the powers that the provinces have, and that the federal government cannot encroach on. However, any power that is not enumerated, belongs to the federal government.
In US, it is the other way around - the constitution enumerates the powers that the federal government has, and everything that is not on the list is up to the states. And the constitution even has a specific clause (10th Amendment) that reinforces that arrangement.
For example, the constitution says that the federal government has the right to regulate "interstate commerce". Originally, this was actually supposed to allow the feds to prevent the states from impeding commerce with other states (e.g. enacting tariffs on out-of-state goods etc). Over time, it became used instead by the feds to prevent or regulate the trafficking of some goods between states (e.g. the National Firearms Act did it for guns in 1930s).
Then, finally, the meaning of "interstate commerce" was reinterpreted to mean any activity that can have a causal relationship on interstate commerce. The decision that sealed this was in a case of a farmer growing wheat for personal consumption (to feed farm animals), in defiance of the federal law that limited production of wheat. The farmer argued that, since the wheat didn't leave his farm, it was not commerce at all; and most certainly wasn't interstate commerce. The Supreme Court ruled that it was, because growing wheat for himself meant that he wasn't buying it on the market, thereby affecting prices, and that this effect crossed state lines - and that therefore Congress was in its right to enact a federal law prohibiting the farmer from doing that.
https://en.wikipedia.org/wiki/Wickard_v._Filburn
Since then, this interpretation has been broadly used to regulate a lot of things - obviously, under this interpretation, pretty much anything is "interstate commerce". The most obvious example is the federal drug prohibiting private possession and consumption of drugs.
"you are influencing the market"
"i'm not taking part in the market!"
"yes, by not taking part in the market, you are influencing the market"
What this means is that when there's a case where the courts have to rule on constitutionality of some law, they err on the side of ruling it constitutional, if there's any way to twist the wording such that it would allow the law - even if the legislators didn't think of that originally. The idea is that the laws enacted by duly elected legislators represent the will of the majority, which is sacrosanct in a true democracy, while the courts are not elected.
Thus, the balance has to be in favor of the elected institution, and the courts have a duty to try to "save" any law by coming up with creative interpretations of the limiting clauses of the constitution. Oliver Wendell Holmes, the Supreme Justice of the Progressive Era (when that concept was at its peak), summed it up as, "a law should be called good if it reflects the will of the dominant forces of the community, even if it will take us to hell".
That doctrine has been on the decline since the Civil Rights era, where SCOTUS was striking down state laws left and right as unconstitutional. But it still surfaces occasionally - e.g. in the recent decision on the constitutionality of the Affordable Care Act, and specifically its provision that requires people without insurance to pay a fine (https://en.wikipedia.org/wiki/National_Federation_of_Indepen...). The court said that the fine is a kind of tax, even though the text of the law uses the term "penalty" consistently, and the legislators that originally wrote the bill explicitly stated that it's not a tax back when it was under discussion (and its opponents insisted that it was a tax, ironically)
So that doctrine kinda explains why they were willing to come up with such an obviously contorted interpretation. What's more interesting is why it stayed with us for so long...
Other than that, you aren't missing anything. A significant chunk of federal laws since that decision was based in part or in whole on that interpretation. There is exactly one court case where that power was found insufficient:
https://en.wikipedia.org/wiki/United_States_v._Lopez
"The government's principal argument was that the possession of a firearm in an educational environment would most likely lead to a violent crime, which in turn would affect the general economic condition in two ways. First, because violent crime causes harm and creates expense, it raises insurance costs, which are spread throughout the economy; and second, by limiting the willingness to travel in the area perceived to be unsafe. The government also argued that the presence of firearms within a school would be seen as dangerous, resulting in students' being scared and disturbed; this would, in turn, inhibit learning; and this, in turn, would lead to a weaker national economy since education is clearly a crucial element of the nation's financial health."
SCOTUS ruled that it was a connection that is too remote. But even then, the ruling was 5-4 - in other words, 4 judges believed that the rationale above is sufficient to accommodate the Commerce Clause!
The problem with getting rid of this ruling is political. Since there's so much federal legislation that is only possible because of it, pretty much every political force (other than perhaps libertarians) has a stake in the game. For the liberals, if Filburn goes away, then so do important parts of the federal Civil Rights Acts (per https://en.wikipedia.org/wiki/Katzenbach_v._McClung), which prohibit discrimination of customers and employees on the basis of race, gender, religion etc. For many conservatives, overturning Filburn is undesirable because it would gut most federal drug laws (per https://en.wikipedia.org/wiki/Gonzales_v._Raich).
But they're still bad justifications! This whole "judicial deference" thing runs counter to the fundamental reason why written constitutions even exist in the first place, IMO. So I wouldn't call it protecting the integrity of the constitution - quite the opposite, in fact, I think it leads to an inevitable conclusion that constitution is just something unnecessary that gets in the way of things.
States and provinces are both unitary states. Lower level divisions of those are creations of the state. County and city governments only exist because the state says they can.
It’s nothing special.
And yet, it's happened before, and will happen again.
It's very much like the EU: Each state is independent, and there is an overall governing body - the federal government, which for the most part can't tell states what to do, it can only give or withhold money to induce them.
There are specific rules about what the Federal government can and can't tell a state.
One difference that does exist is military, where EU states can have a military (as far I know), but US states can not.
Not so. US states cannot have a standing army without consent of Congress. The Congress has given such consent in the form of the Militia Act a century ago, which enabled the states to create the National Guard and the State Defense Forces / State Guard.
And while NG can be federalized (i.e. put under the federal chain of command, with the president as commander as chief), SDF are not - their chain of command terminates with the governor, and they cannot be used outside of state boundaries.
Most people in US know about the National Guard, but not about SDF. It's largely because the latter is rather small and obscure, and mostly used as a sort of civil defense agency with a military chain of command (many states don't even arm their units). But it's an interesting system: https://en.wikipedia.org/wiki/State_defense_force
EU states are nation states, US states are not. The EU is not a nation, the US are.
EU states have much more sovereignty than US states written inside laws, but more importantly, through support of their people. This is why there is a Euro crisis and why Brexit happened: The unification of Europe is a beautiful idea and I personally hope it will recover, but while subsets of it were considered as one nation at some point (Austria, Germany etc.) the EU as a whole simply never was and never will be.
The EU, despite its name, is essentially a humongous cooperation deal between countries. It has many of the trappings of a nation, but that's an illusion. EU countries are sovereign (consent is required in any alteration of the membership rules and they can leave at will) but US states are not. That's the theory. In practice, the differences are even bigger: There's no EU patent system, for example.
I think the EU is becoming (and in some senses arguably already is) a quasi-state. Hence Brexit. That's kick back.
And there is now an EU-wide patent system: https://www.unified-patent-court.org/
Even that is a little shaky, as historically there were organized state militias, which eventually evolved into the National Guard. Even now, the National Guard formations for each state are under the direct control of that state, rather than directly subordinated to the federal government.
In fact, the little rock five were escorted by federal troops facing off against state controlled troops.
The latter also require Congress authorization, in a sense that the state is not allowed to create them without Congress "consenting" (e.g. via legislation):
"No State shall, without the Consent of Congress, lay any Duty of Tonnage, keep Troops, or Ships of War in time of Peace, enter into any Agreement or Compact with another State, or with a foreign Power, or engage in War, unless actually invaded, or in such imminent Danger as will not admit of delay."
But the Congress only has the power to grant or withhold such authorization; control still remains with the state. And, of course, the states can still have their militias - so long as the state does not explicitly organize them, it's not "keeping troops".
i think that's kind of exaggerating the situation a bit. They maybe have a bit more control over their own affairs than most country's provinces do, but the degree of autonomy a province has varies quite a bit from country to country. there's nothing that fundamentally make a state different to a province besides the name, and comparing a US state with an EU member nation is just silly.