So K-complexity is largely a theoretical notion, I have no idea why people love it so.

Imagine some Oracle told you that obtaining the ultimate theory of physics - the one that unifies relativity and quantum gravity, and all that - was impossible. Then following your logic you might conclude that it was pointless to study physics, since one can never obtain the perfect theory. But that would be wrong; it would still be highly worthwhile to attempt to obtain better and better physical theories.