the quality of the music always takes precedent over the quality of the recording

With a doubt!
Of course the reason why some non-studio recordings are so good (musically) is precisely because they are live performance recordings.

Personally I think that with digital editing being so easy, a performer can afford to take risks in the studio that they might not dare in a public situation, with the attendant potential for an exciting performance.

Certainly given the choice of a musically good take with fluffs and a boring but technically perfect take, the sensible engineer goes for the more exciting version and fixes the mistakes (possibly with material from the other take)

Anahata