How authentic is it to release something the artist does not think is representative of what he wants to portray? In other words, if there are all these mistakes in there that make the artist cringe every time he/she hears them, the recording is obviously not representing the artist in the way that he/she thinks is right. It's my record, dammit, it should sound like what I want it to sound like, right? A novelist never releases a book without editing, re-writing, etc. Why should music be any different?
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Back to this: How authentic is it? Perfectly authentic! A mistake is a true reflection of something that's going on inside. Of course, we don't want people to know about our shortcomings and limitations. So we alter the recording to match our desire to be mistake-free, or as close to the ideal as possible. Then we find that if too much of that stuff is taken out, it starts to sound less human. Nobody's perfect, after all.
I have come to one conclusion: recording's a bitch! But it makes you confront a lot of stuff that you wouldn't otherwise.