Water is much more complex than the characteristics we typically test. The usual tests may be "perfect", but fish still do not thrive due to the presence or absence of a mineral not tracked. The Niigata breeders have had generational knowledge that ponds fed by the waters of a particular mountain are better than ponds elsewhere. It is all melted snow and rainwater, but it has flowed over and through different soils and rocks, and has been changed. We can duplicate the parameters for which we test, but that does not mean the water is the same. It only means the pH, alkalinity, iron, etc are the same. But even then it may not really be the same, because the form of the iron present in one body of water may differ from that of another, but the amount detected by a test is the same...but it is really different ferrous/ferric molecules.
I think TomC is correct that everything on his list is a contributing factor, but no list is going to be complete.
I think the first step for the koikeeper who has progressed to the point of truly being concerned about water is to decide whether his/her source water is acceptable or not. If it is acceptable, then the goal becomes to maintain the pond water in a condition as close to the source as can be done. The task is not easy, since deterioration begins the moment it is added to the pond, but water changes (or constant flow) can accomplish much of the task. If the source water is not acceptable, the hobbyist has to decide whether they are willing to devote the continual effort required to re-create the water and maintain the characteristics of the re-created water on a constant basis. For example, a reverse osmosis system may be used to produce exactly the water desired, but it will do no good if membranes are allowed to become blocked or if used only sporadically. Fluctuating water is bad water, no matter how "good" the test readings at the limit of the pendulum's swing, because that just magnifies how "bad" it is when the pendulum swings to the other side.
Stability is important to the fish, even if the Boron content is slightly less than some ideal decided by somebody.
....In Florida, like elsewhere, we complain about the tap water. The same water, without chlorine, is sold as Dasani, Zephyrhills, etc., etc. Sometimes we do not appreciate that our greatest asset in fishkeeping is the simple tap, and not the showy filter. [Of course, I do wish the pH was lower and the hardness less.

]