Just to refresh you how ISU define these three in the more easily accessible language:
• Performance is the physical and emotional involvement of the skater/couple as they deliver the intent of the music and composition (e.g. carriage, style, personality, variety, contrasts, projection).
• Composition is an intentionally developed and/or original arrangement of all types of movements according to the principles of musical phrase, space, pattern, and structure (e.g. idea, concept, unity, pattern, phrasing, originality, design)
• Interpretation of the Music /Timing (for Ice Dance) it is the personal, creative, and genuine translation of the rhythm, character and content of music to movement on ice.
In what way these three components can be construed anything but a clear intention to reward artistry as a prime motive?
A lot depends on how you define "artistry" or "artistic." It seems that sometimes the word gets used to mean not much more than "visually pleasing" which to my mind is not the same thing.
To me, artistry implies intention. Therefore the Composition component seems to be the most connected to artistry in my mind, but the intention may belong more to the coach or choreographer than the skaters themselves.
For example, the "Carriage & Clarity of movement" criterion under Performance seems to me to be primarily about technical form. It may be achieved with intention, or it may just be a by-product of good technique. Same for "Spatial awareness between partners." And poor execution of those criteria is more likely a result of weaker technique than weaker intention. The other Performance criteria are more about the skater's intentional performance.
The first criterion under Interpretation is "Movement and steps in time to the music (Timing)." Again, it is possible to achieve that mechanically without any additional artistic intention as defined in the other Interpretation criteria. It is also possible to have all the interpretive intention in the world but to fail at skating in time to the music because of technical deficiencies that prevent the skater from controlling the rhythm of the moves.
So sometimes skaters try to be artistic but resulting performance deservedly scores low on some of these components.
Other times skaters just go out and skate well (cleanly and confidently) to whatever they were given to skate to and as a result earn high scores for Performance without any intention to be "artistic."