You really need to rethink your biases, though I know you won't (you've made that abundantly clear in post after post, anonymous or attributed). You're SURE you're right. Maybe that's what it means to be left-brained, in which case I am thankful that I am whole-brained. I have successfully completed graduate degrees in literature,educational psychology, and mathematics education. And I continue to learn in as many areas as I can, in whatever ways I can, without needing to insist that there's no place for rote, but merely that it isn't the best option for many sorts of learning. Would that you could see past your nose.
Wasting time is very much relevant to the tradeoff between rote processes and conscious understanding (and not just when it comes to muscle training).
The acoustics of speech can be understood, involving lots of interesting patterns. Why not consciously analyze the speech signal we receive when people speak to us rather than doing it by rote?
Why not conduct etymological deductions rather than rote memory lookups when listening or reading?
Why not do conscious applications of the parabolic trajectory law every time we try to catch a ball?
Why not translate all arithmetic problems into their set theoretic underpinnings?
Alternatively, one could handle these things as the Quadratic Formula used to be handled in traditional math. Have the students derive it a few times on their own (no Reform Math algebra book I've seen has students do this very important activity, preferring formula memorizations and guess & check plug-ins) and then move on.
One might also explore the Strawman-free middle ground between "practice MUST precede understanding" and "understanding MUST precede practice," and make decisions based on feedback from students and student performance. And, doing our best not to impose our "prejudices and learning styles" on "everyone we try to instruct", keeping our minds open to what might be holding them back versus helping them forward.