> Random k-SAT is useless

Other than cryptography, is there any real-world value in solving random problem instances of NP-complete problems (at least when average case approaches worst case, based on the parameterization of the problem)? Presumably these are instances that do not have any underlying mathematical structure as a truly random problem instance is Kolmogorov-maximal, and thus even if you solve the problem via brute-force, the result still isn't useful for any predictive purpose.