We shouldn't "memorize" the times tables,

While I agree with your sentiment, times table memorization is necessary to build a skill that will be needed later in math. It's good to teach the basis of the times table but if you don't have it memorized, every later math problem will be slower to solve because you will be focusing on the principles of how a times table works instead of the new concept like how to multiply long number with carry.

This is related to my pet peeve, that despite it being 40 years ago is still burned into my memory. I had many Physics professors who would talk about not needing to memorize formulas for exams because they could be derived from first principles. Those same professors were always the ones who would give exams that if you didn't have formulas memorized, there wouldn't be time to finish.