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Even bog standard classical mechanics can be very complicated and unintuitive, once you go to things like Hamiltonian dynamics and many-body problems. Then you have statistical Physics and, as you said, relativity and quantum mechanics. I’ve recently spent some time learning about some quantum gravity theories; these things are hard.

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Yes. Chaotic systems arise in classical mechanics. So while often the formalism is easier to write down than for example in general relativity, calculating a solution is often very difficult or practically impossible.

It's probably worth distinguishing between conceptually simple and mechanically simple. A many body problem is easy to understand (relatively), you're just extending existing rules onto more things at once. Now, actually calculating a position at a time given some initial vectors? That's complicated.

You’re right. But many-body can also turn into statistical physics, which is quite complicated conceptually (basically when entropy and ergodicity become important). Then you have the best of analytical Mechanics, statistics, and quantum mechanics if you fancy.

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