Makalakumu, I am curious what principles you want to teach that are being obscured by the practice of too much basics.
From my perspective, the ideal teaching method juxtaposes basics, drills, and requirements so that they in fact teach the principles of our systems. It's merely a matter of picking what the principles and related practical outcomes are that we want our students to learn and then designing a well-connected series of lessons to teach them.
For a concrete example, let's suppose that we want white belts to learn how to get off-line from a linear attack to the outside, to block and simultaneous check for safety, and finally to counter quickly with their own strike(s). This is our core theme for the white belt, and the more specific we get, the easier it is to design supporting drills to achieve the goal.
So what are the basics a student minimally needs to accomplish this?
(shortened) front stance
stepping forward and backwards at a 45 degree angle
low block
middle block
high block
lunge punch
(maybe) a front kick
All these techniques are found in isolation within variations of the taikyoku/kihon/kicho kata/hyung used in various Japanese & Korean karate/TKD/TSD styles. Most do not step or slide backwards on the initial 90 degree turn and block - a few smaller styles do - but I regard that as a minor alteration for our purposes.
Now how about we break this up into a series of lessons.
Lesson 1
the front stance and its shortened version for practical use
stepping forward and backwards with hip turns
the lunge punch
Lesson 2
review
refinement on hip turning
the low block and the high block
practice lunge punch on a partner held target
Lesson 3
review
questions?
stepping forwards and backwards into a 45 degree front stance
front kick
practice lunge punch and front kick on a target
Lesson 4
review
middle block
practice low, high, middle blocks with a partner, no moving, emphasis on using hip motion for power and angling
And so on. With each increasing lesson up to a maximum of 30? we introduce more and more drills that teach the stepping off line. We discuss going inside and outside of an attacker and why outside is 'safer' but we also tell the students the disadvantages of each position relationally. We discuss and practice the footwork extensively, relating them to other sports and physical activities as needed, showing the point that karate is not some mystical Asian thing - it is based on solid biomechanical movement. We practice one steps, formal and informal, that end with the defender stepping off to a 45 degree angle and then countering with a punch or kick developed in previous lessons. At some point we teach the kata, also explaining that they are solo vehicles for developing form, but they are incomplete without serious partner-based practice as well.
Fleshed out with stretching, calisthenics, and other traditional karate training methods, we could easily take up to 3-4 months to teach all this at 3+ classes a week and yet not bored the average student IMO. At the end of this span the student will be well grounded in a concept that will translate well into sparring at the next belt level, and they'll have learned in a reinforced fashion, a key idea which will be built upon increasingly.