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> Compressed sensing in this context is made possible by the fact that the signal’s frequency content is highly sparse.

The fact that the signal is so regular is what makes this possible. You're sampling the same signal many times, far more than twice the frequency of the highest frequency.

If the signal's frequencies changed over time or if there were more frequencies in the signal, this wouldn't work or would require far more data.

It was, but the goal isn't lossless recovery it's good enough recovery either in an L1 minimizing sense, or some other criteria

The nyquist limit is based on recovering a general signal. If you have a-priori knowledge about the signal you can do much better.