Any "system" follows some logical rule. Most of the systems I have seen, such as Yoshinkan, seem to follow a very linear idea of "system."
This is very interesting since by your own admissions you have not spent much time under Yoshinkan training methods.
There was something very interesting in that article by Takamura:
On the bad side, it can lead a student to dismiss a technique or concept as invalid just because he has not put in the time to learn it properly or delve into its secrets. Students that fall into this trap never master their basics. Later in their training you find gaping holes left by ignoring important lessons that the student chose not to pursue because he couldn't see the value in them.
From my experience in methods that have a systematic approach to training I'd say that the systematic aspect is designed to address the foundations and basics thoroughly to avoid the problem Takamura highlighted. The same trap that he alludes to above regarding gaping holes in the basics I have found to be extremely prevalent in those who practice entirely from a "chaotic" model for lack of a better word.
From my experience the systematic method is used primarily in the beginning stages to assist the student in understanding what defines Aiki waza and what governs the correct and effective execution of technique. Elements of tai sabaki, timing, kuzushi, body structures, ma ai, metsuke, kamae etc. are learnt and forged here and it defines the foundation of the Shu aspect of evolution. However in the systematic methods I have experienced, this way of training is just the beginning and is developed upon in randori training to evolve out of the rigid structure of the system towards a more spontaneous expression of one's Aikido. The good thing here is that these persons will execute spontaneous technique in randori (even with resistance) often without losing most of the fundamental elements that are prerequisites of effective and sound Aiki waza. The reason is because these elements have been systematically drilled into the mind/body of the individual in every class so they know precisely what is correct and what is incorrect movement even if/when they make a mistake.
In my experience the folks who utilize the chaotic pattern only are oftentimes those who can only execute the spontaneous waza on fully compliant uke, else the entire technical foundation goes to hell. The reason is often because the fundamentals are often cloaked within the practice of kata in the early stages so there is no demarcation between technique (kake) and the constituents required to make said technique effective in a spontaneous environment (tai sabaki, shisei, ma ai, kamae etc).
My personal belief is that too much of either approach has flaws. The best approach is found in a balance betwen the extremes. I think Ueshiba M. had a pretty chaotic approach to instruction from what I've read, i.e. there may have been no real logical process to what was being taught, he merely expressed himself based on how his spirit guided him. What made things easier for him however was that all of his students already had most if not all of the basics inherent in Japanese Budo covered, being Dan grades in other Budo before coming to study with him.
This thread reminds me of when Bruce Lee spoke about systems and how they limit the individual's expressive ability. The thing is however, I wonder how much of a work of martial spontaneity and expression Bruce Lee's Jeet Kun Do would have become without the solid foundation that came from his earlier systematic training in Wing Chun.
Just my thoughts.