The Missing Gem.

I do not believe that Karate has a single strategy that can be summed up, some Kata call for direct strategy, some call for something less direct, the tactics fit along the prescribed lines of each.
There is a major clue to principles and scope to which Karateka must pay attention if they are to gain anything, rather than wondering why they have wasted their time for so long only to remain fixed at a particular phase.

Seipai has few direct punches, Seiyunchin has few direct kicks and still, few direct punches, what does that say about strategy when this is taken into account? On the other end of the spectrum (coming from a Goju Ryu Background) you have Gekesai, which is extremely direct, you also have Seisan which is both direct and indirect.
Still, you could also say that Gekesai is indirect and Karate DOES have a single strategy that sums everything up, it depends upon the individual perspective and how particular things tend to speak to each person.

Understanding strategy, however, is necessary for deeper understanding; a depth that is what many may call borderline 'esoteric,' though what we end up with in our modern Dojo is something that is borderline 'schizophrenic.'
Not in all cases, there are some excellent Teachers out there that have a truly deep understanding of strategy, their own personal strategy deeply rooted in a base idea that was seeded as their foundation long ago, something modern Karateka seldom experience in the majority of our community.

What if each system of Jujitsu were reduced to a single Kata, then set up in sequential order as part of the cirriculum of a single school? Would something not be lost? Furthermore, what if nothing was thoroughly explained or explored? The drills would have very little, if anything, to do with the actual principles at work in these Jujutsu Kata.
Then you have tenth dans that proclaim knowing 27 different Kata and performing them, but do they really understand them?
Now the dilemma is spelled out, the case is clear; some would laugh at the notion of only practicing one method, like Atemi Waza versus Ne Waza, or two methods, saying that one needs to know all 27 superficially in order to be recognized within the community as a competent practitioner or Teacher.

Karate is having an identity crisis, split personalities exist under one roof and they have gone undiagnosed.
Were this not the case then we would be seeing courses offered in the 'Seipai Method' or the 'Gekesai Method,' there would be a much more open-minded approach to accepting the '(Insert Name Here) Method' following the path of Shu-Ha-Ri, while having good foundations in a couple other methods.
Again, there is no such thing, systems fall apart once they are deeply explored and, from this, new systems are meant to emerge.
You may also have a uniting factor with courses in Violence, with things like Rory Miller's Matrix of Violence used as a measure, Marc MacYoung's 'question everything' mentality, his field stripping mentality (which is VERY lacking in many Karateka these days) would be the norm.

Little nuances may not be the point, but they are definitely a tool toward understanding, and every tool has its' place in the Dojo - that is the true nature of Hojo Undo, or supplimental exercises/training.
It does not just end with the Chi'ishi, and there is another way of utilizing strategy from one thing to shed light on others.