Most of this is noise if one does not focus on the fundamental relevance of Kolmogorov-Smirnov tests. Executing a test is a simple technical act, not a concretization in itself; the value lies in the discipline with which hypotheses are formulated.
Without a rigorous framework, the test can produce statistically valid results but operationally meaningless.
For example, comparing the distribution of returns of an Australian regulated pension fund by APRA with that of an unregulated hedge fund would not provide controllable insights for the investment strategy.
Only a relevant application of the test, taking into account local constraints and market conditions, can be considered a true concretization.