I think in some ways you're tyring to compare the wrong things. For example, you're setting up the analogy original painting:a print as performance of a play::a different performance of the play. I think a more analogy is original paiting:a print as performance of a play::video tape of the same performance (or seeing live music::listening to a CD). I think you'd agree in that case that the dichotomy of impact between the two is pretty analogous. Watching a play on video tape is as different from watching it in person as seeing print of a Van Gogh is from seeing it in person.
Now, there is an analog in painting to the common practice in the performing arts of the constant (and necessary) reinterpretation of the original piece (i.e., sheet music, manuscripts, etc.). Rather than prints, people do reproduce, by hand, a work of art. Go to any major museum and you'll find aspiring artists galore copying works. Or take the case of these two works, the
first being a reinterpretation in abstract sculpture of the
the second.
Of course, this is fairly uncommon, and even more uncommon for such a copy/reinterpretation to become as recognized as the original. I suppose that's because in painting, the original is already in its final form, nothing more needs to be done for a viewer to experience it as the artist intended. Whereas with plays, music, etc., there needs to be a second, interpretive step from one medium (written) to another (performed).
Of course, a similar thing exists in painting, and is far more commonly seen, and that would be multiple people painting the same subject.