I had also studied tai chi before i took up aikido. actually, i took up aikido because i could find no good tai chi classes in my area after moving back home from abroad. i am quite happy with this choice, i found that the one aids the other, and i still remember my long form tai chi so i can do that at home.
i noticed the same as you, although our beginners class (up until the first grading) was fairly linear and syllabus oriented, i found that after we joined ordinary classes the teaching style was more or less like you described.
we have the syllabus for our next gradings pinned on the wall and it is our own responsibility to memorise them and to learn them, that means that we have to "nag"
the sensei to show us. usually he puts aside 15 minutes at the end for syllabus training.
A grade syllabus usually consists of 5-6 techniques. Memorising the names helped me greatly.
whilst the matrix of aikido appears complex at first, there are only 5 basic techniques that i am being taught at the moment. variations are countless though, but i find that this style of teaching keeps me sharp and aware. after about 2 years of training i have now a grasp of it and can follow most of the new techniques i am being shown, BECAUSE i have done so many variations.
and, as mentioned, there is system in the chaos.
time, man.. time.
grasping the birds tail,