How do blue book exams translate to real world problems the students will encounter? Why not open book + AI use exams, because that's what students will have in their careers?
There are many subskills that you must be proficient in without tools, before you can learn more interesting skills. You need to know how to do multiplication by hand before you rely on a calculator. If you can't do multiplication with a calculator, you're not going to be able to make sense of the concepts in Algebra.
I never need to "fall back" to the principles of multiplication. Multiplying by the 1s column, then the 10s, then the 100s feels more like a mental math trick (like the digits of multiples of 9 adding to 9) than a real foundational concept.