I think I'm in the minority among coaches and fans, but here goes:
Art and sport are inherently mutually exclusive.
Art is, by definition, completely subjective. The quality and beauty and meaning of art are all in the eye of the beholder. To attempt to quantify "artistry" is blasphemous (for lack of a better term) against the very concept of art, in my opinion. Sure it can be studied, evaluated, and taught, and specific techniques can be practiced and perfected, but at the end of the day there's no objective way to evaluate the quality of a work of art.
Sport is, by definition, objective. There are winners and losers. Everything can, should, MUST be objectively evaluated and quantified. Either the ball went through the goal or it didn't. Either the runner crossed the finish line first or he didn't. There is no room for interpretation. This is not to say referees never get it wrong; I'm simply saying that, in principle, sport is built on objectivity.
So which is gymnastics? It can be either one. It can be a performance art, like dance, juggling, circus acrobatics, etc. Or it can be sport, like football, track & field, or handegg. But when we try to be both at the same time, both the art and the sport suffer.
This is not to say that it couldn't split into two different disciplines, say, artistic gymnastics and competitive gymnastics; however, I think by trying to do everything at once, we cause the sport/art to fall short of its potential in both categories.
EDIT: Also, there's a second reason I don't like the evaluation of artistry, and that is that it is so often used as a coded way of talking about body type.
For example, compare Shawn and Nastia. Shawn kept her chin up, moved her whole body to the music, and was in every way extremely expressive, but nobody ever refers to her as "artistic" because her body was short and tanky. Nastia had "talon wrists" in everything, never moved her head with her dance, and in general looked like a praying mantis out on the floor, and yet people always said she was "artistic" because her body was long and lean.
And I vehemently object to any sort of evaluation based on the body type of the athlete.