Systematic methods are also quite effective at building the basic non-technical foundations that allow Takemusu Aiki to be possible. Often too much attention is placed on technique itself instead of what factors enable the individual to get into a position to execute sound, successful technique and also be able to adapt instantly and produce the right technique as determined by the situation.
It's sort of like developing a master key through the development of different core principles. Once you have the master key the nature of the lock is irrelevant, it will be opened.
Like Yoshinkan, our method also has a group of basic systematic drills (Kihon Kozo) that are designed to develop different aspects of aiki waza and ability separately from the practice of technique or kata itself. From the little Yoshinkan training I did I actually felt quite at home with the fundamental drills because most resembled the stuff we do at the start of class.
Of course one can do this without sysematic training, but the question becomes how long does it take, how do you gauge progress and how do you know you may not have missed something?
Just my 2 cents.