Back in the folk-boom sixties, there was a popular phrase, "Ragged But Right." I believe some artist even used it as an album title. The idea is that an unpolished performance style is preferable to a too-careful emphasis on precision, and that musical performance should, first and foremost, be a vehicle for human expression.

Of course, the "but right" part is an admission that everything "ragged" is not necessarily good ~ the trick is to relax one's standards of musical precision only as a way to allow brilliance of a higher order to come shining through.

Very often, a musical phrase featuring a note or two that is sharp or flat or mis-timed (when measured by conventional standards) is a superbly eloquent bit of personal expression.

From the listener's/audience's point of view, this element of musical appeal is more accessible in live performance than from recordings, but that does not mean that recording can't convey any degree of personal warmth, intensity, etc. It's just that it's more difficult for recordings to convey such subtle and mysterious elements than for live appearances.

From the performer's perspective, one needs to realize that allowing one's heart and soul to be revealed is more important than obsessing upon speed of fingering, purity of tone, etc. Simple enough ~ especially when compared to the recording engineer's response to this question, which is much trickier.

Even though the act of listening to a record cannot compare to the experience of live performance, a certain limited degree of that ragged-but-right "magic" can be captured and played back, and every recording should try to convey such meta-musical communication to the greatest extent possible.

How? I dunno; I'm an audio-tech illiterate...