Not even close. Nyquist requires sampling at least twice the /bandwidth/ of the signal, not necessarily twice the highest frequency, because of aliasing. For example, a signal that’s 1 megahertz +/- 1khz requires only 4khz sampling to capture the detail.
Aliasing is always a factor because no real signal has a highest frequency nor a fixed bandwidth (noise is never zero, and all filters roll off gradually forever)
I think it's a bit harsh to say not even close. I think it captures the idea pretty well.
The reason it's not perfect is because of your example, where a signal is not baseband. The extra leap required to understand that is amplitude modulation and demodulation.
Notice that to reconstruct the original signal of your example, you need to know the samples which are collected following the hypothesis of the sampling theorem, and you ALSO need to know the magic frequency 100MHz so that you can shift up your 2kHz bandwidth. That's the same setting as modulation.
The only concept missing, then, is recognizing that sampling can perform demodulation.
Demodulation via sampling isn't a weird side-case, that's at the core of understanding Nyquist and doesn't line up with the intuition that you just need to "sample each up- and down-deflection of a wave at least once"
I disagree with you. To be clear, "sampling each up and down deflection" is exactly the right idea in the case that you have no other information besides the samples (and besides knowing the hypothesis of the sampling theorem is satisfied). To use the more general version of the sampling theorem, you in addition need to know the center frequency (100 MHz in your example), otherwise you cannot reconstruct the signal. So already the setting is slightly different. You need an additional assumption.
All real signals have limited bandwidth, including noise.
Assuming there's no external source of radiation, I can absolutely guarantee there is no energy propagating at cosmic ray frequencies in a circuit built around an audio op-amp with standard off-the-shelf components.
No lowpass filter or circuit attentuates any frequency to zero, including your example. The attentuation will be 10^(-huge number), but it wont be zero.
This isn't just pedanticism, you really can't just sample at 2x the corner frequency of your circuit.
(Unless there's some quantum effect that gives a minimum energy level possible for a signal? But even then it would be probabablistic? Is this what you mean? I didn't pay close enough attention in physics class)
Aliasing is always a factor because no real signal has a highest frequency nor a fixed bandwidth (noise is never zero, and all filters roll off gradually forever)