Distribution tools are for espresso, not pour over or immersion brewed coffee. In espresso, you have extremely high pressure, so if there is a density differential in the coffee cake, you will get most of the water flowing through the spot that has the lowest density, and the rest of the cake will not be visited, making for a weaker drink.
Also, the "recipes" are usually just a ratio of coffee grounds to boiling water by mass, a rough idea of how fine to grind, and a brew time. If you take these parameters and vary them by any reasonable amount, you will definitely taste the difference.
Overall, it's not an apt analogy. There is no "fidelity" for coffee like there is for audio. There is a quantitative loss function you can define for audio quality - just the sound you're trying to replicate versus the sound that your system actually ends up generating. For example, no human ear can hear frequencies above ~22kHz, meaning anything over the normal ~44kHz sample rate provably makes no difference.