Vitanyi and colleagues have a paper where they show that although K(X) is uncomputable, in practice, you can attach a probability to one X having greater or lesser K(X) than another X (to ridiculously oversimplify; K(X|M) might be better notation). This is kind of analogous to p-values and is related to the statistical interpretations of Kolmogorov complexity. The uncomputability is important but is not the intractable obstacle it seems like if not elaborated on.