I generally agree with you and your opinions on kata, but I don't see this. Modern art.. art in general, really... puts some of the responsibility on the viewer. There are elements within art that are not subjective. Taste can be personal and subjective, but when you look at a painting of a line on an otherwise blank canvas, it matters where the line is, how the line is drawn, how thick or long that line is. What color is the line? What color is the background? All of these things have an effect. Tension, balance, contrast, color temperature. These are things that are all able to be identified consistently and objectively. In order to appreciate those things, one must learn to see them, and also understand what they mean.
The interpretations of these elements, coupled with some knowledge of the artist's intent behind them, can lead to interpretations such as, "the powerlessness of the common man." In some cases, without knowing the context of the art piece, you will miss things like irony, which could be very important to the piece.
The same principles apply to all art, including commercial art. Graphic designers are skilled at using objective, consistent principles to create designs that evoke emotions or feelings. Tension, for example, is often about where objects are placed on a page, how closely they are together. How close they are to the edge of a page. Sometimes, a designer will create a sense of unease on purpose.
In the same way, I believe, the proponents of kata would say that the onus of understanding the kata is on the practitioner, but that the value is objective, repeatable and consistent.