[TheOtherHobbes]

No, you're confusing two things. The uncertainty in a Fourier transform applies whether it's continuous or discrete. It does not require sampling. It still appears in the sampled DFT, but that's an extra wrinkle. It's a feature of the transform itself, not the sampling process.

You're also confusing horizontal and vertical resolution. Sampling bit depth sets the maximum possible dynamic range resolution of both pre-transformed samples and post-transformed frequency components.

The number of samples defines how many frequency components there are. The number of bits define how accurate their levels are.

The uncertainty trade off is in the number of samples. You can do an FFT on multi-second chunks of music. You get superb frequency resolution, and it will transform back to the original. But you can't use the spectrum to see fine detail in individual notes, because the frequency domain view is just a bar graph with the same number of samples, and shorter features - like individual notes - are smeared out across the entire frame.