Analogue recording never was and never will be "a perfect representation of the original source". Analogue recording adds stuff like hiss and jitter. That's one of the reasons why the recording of classical music switched to digital recording in the early 1980s, as soon as digital recording became viable. These recordings were released on LP (before there were CDs) and everyone thought they sounded better than the best analogue recordings at the time.
An interesting collection of recordings is Murray Perahia's recordings (with the English Chamber Orchestra) of the Mozart Piano Concertos. This was a cycle that was recorded between 1975 and 1988 sort of halfway the recording project CBS Masterworks (now Sony) switched from analogue to digital recording. I have most of the recordings on LP and the whole set on remastered CDs. It's very interesting that the original LPs that were digital recordings sound better than the analogue ones. And it makes it very understandable that recording went from analogue to digital. On CD you really hear the limitations of analogue recordings.