It appears simple if you have a simplistic understanding of how things work. There is nothing "infinite" about analog recordings. Not even remotely. That you assign an infinite to them shows lack of understanding. That you think digital discards things, while analog recordings do not just shows more lack of understanding. Attacking me for holes in your knowledge is not a good look. I seem to know exactly what timbre is, I just don't feel a need to attach special qualities to it beyond what it is.
Analog instruments don't sample...analog/infinite - very simple concept; granted within the bounds of manufacturing and human hearing but nothing is "discarded" or "sampled' like in digital.