I am in full agreement with you, Sam. Divide-and-conquer it is.
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Perhaps interesting to tell this part of the story.
The Founding Fathers were good students of investigating what other nations had done in their days. Two countries were interesting for them in particular, because they were (con)federations: Switzerland and the Netherlands. Switzerland still is a confederation.
The Founding Fathers did not want to do it the same way these other countries did, because they heard that you then end up with countries the size of Switzerland and the Netherlands. The Framers wanted a much larger nation/(con)federation.
In these little countries, the power structure was as follows:
1/ cities and lands
2/ cantons or provinces above
3/ (con)federal agreements between the cantons or provinces on top of that.
A bottom-up approach.
When looking at the US Constitution, and you point this out, too, we see that they were particularly interested in 2/ and 3/ meaning the States and the Federation. You can tell that the Framers inverted the model and instead of it being built up from the ground, they 'built' it down from the sky. They inverted the power structure, made it go top-down.
Naturally, they could not let that hang in the sky, and so they based it on We The People. The sovereigns in the US Constitution are indeed the People. Notice, too, that they skipped 1/ cities and lands (cities and counties).
Next, however, they do not say all that much about the might and power of the People and they focus particularly on what was very complicated for them to put together: The relationship with the empowered Federation and the States, and having to give in to the powers of the States.
So, they were extremely smart, and all will have had self-interests in mind while at the same time wanting to deliver a foundation for a nation they desired to succeed, Enlightened ideals and all.
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One angle I find the most interesting angle is that Thomas Jefferson devised a clean voting system, and yet the States ended prohibiting cities and counties from using it. The States did not want the best possible system.
In Thomas Jefferson's voting system (proportional voting), all voters end up getting the representative they pick themselves; there are no losers.
It's like cutting up a cake based on all votes all at the same time. Twenty-five percent of the votes, then twenty-five percent of the seats.
The powers that be at the State levels did not want their power to be torn into too many directions, so they stuck with winner-take-all that has a group of winners and (large groups of) losers. The real mean powers are therefore concentrated at the State levels. That is where they made their stand against the Enlightened ideals of the US Constitution.
Still, the US Constitution is actually telling States to not deny or disparage the right of the People (Ninth Amendment), and so we are entitled to Thomas Jefferson's voting system for cities and counties (also because cities and counties are not mentioned in the US Constitution, not directly empowered, while the People are directly empowered and therefore superior to cities and counties in light of the US Constitution).
It is a battle we can win, but only if we insist of course that we get our US Constitutional rights that are now taken away from us by the States.