Fundamentally, technique originates and develops within concept (and physique is intimately related). I currently believe that the only way to practice and develop your own, fundamental "technique" or relationship with the instrument, is through practice and acquaintance with the fundamentals of music as they are layed out on the piano itself. The principles that the piano's tuning system is built upon is a kind of puzzle whose pieces can only be conceptually (and aurally) fully gained by practicing and becoming acquainted with them in a fundamental way. In a sense, the only way to play arpeggios exactly as you personally play them, knowing your own specific relationship to that aspect of music, is to practice them fundamentally, outside of the context of a composition. An arpeggio within a piece of music by Mozart, for example, always has a human context which is personal to Mozart's physique and mentality, and the job of the performer is to get inside of the composer's head to understand what that context is. So, ultimately, it depends on what you want.
Composers like Bach, Mozart, Chopin, had this musical puzzle clearly within mental grasp and their music was pulled from it, passing through their musical understanding and personal physique. In a sense, each individual composition (or even a composer's entire output) is only a glimpse or creative representation of the greater context from which their specific musical thoughts were pulled. The entire body of music is still not even a full representation of the greater context from which individual pieces are pulled, so only practicing pieces will at best give you only a glimpse. So, again, it depends on what you want.
The way I see it, either way, whether you are truly wanting to do each composer and their works justice (because in order to do so, you have to not just play their works, but in a sense, see what they saw as the fundamental greater context, too), or whether you are wanting to develop your own relationship with the instrument, knowing the fundamental musical puzzle is essential to a "serious" pianist's playing and arsenal. In fact, I personally believe it's audible when it's there and when it's not.