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I think it is you who have misunderstood the Nyquist-Shannon theorem. Aliasing and noise are real concerns. Tim Wescott explains it very well [0] (Figures 3, 10 and 11). If your signal is below one half the sample rate but the noise isn't, you'll lose information about the signal. If your signal phase is shifted wrt. the sampling, you'll lose information. If your sampling period isn't representative, you'll lose information. These are not implementation details.

[0] https://www.wescottdesign.com/articles/Sampling/sampling.pdf