It’s an analogy. There is actually an academic joke about the point you are making.
A mathematician and an engineer are sitting at a table drinking when a very beautiful woman walks in and sits down at the bar.
The mathematician sighs. “I’d like to talk to her, but first I have to cover half the distance between where we are and where she is, then half of the distance that remains, then half of that distance, and so on. The series is infinite. There’ll always be some finite distance between us.”
The engineer gets up and starts walking. “Ah, well, I figure I can get close enough for all practical purposes.”
The point of the analogy is not that one can’t get close enough so that the ear can’t detect a difference, it’s that in theory analog carries infinite information. It’s true that vinyl recordings are not perfect analog systems because of physical limitations in the cutting process. It’s also true for magnetic tape etc. But don’t mistake the metaphor for the idea.
Ionic movement across membranes, especially at the scale we are talking about, and the density of channels in the system is much closer to an ideal system. How much of that fidelity can you lose before it’s not your consciousness?