Speaking as an “old boomer” who pre-dated New Math by a few years, It wasn’t about calculating in your head or making in more “real” to students. I looked it up:
These curricula were quite diverse, yet shared the idea that children’s learning of arithmetic algorithms would last past the exam only if memorization and practice were paired with teaching for comprehension. More specifically, elementary school arithmetic beyond single digits makes sense only on the basis of understanding place value. This goal was the reason for teaching arithmetic in bases other than ten in the New Math, despite critics’ derision: In that unfamiliar context, students couldn’t just mindlessly follow an algorithm, but had to think why the place value of the “hundreds” digit in base seven is 49. Keeping track of non-decimal notation also explains the need to distinguish numbers (values) from the numerals that represent them.
After all, the guy with the tear in his eye looks more like a right-hander than a right-winger. Speaking as a right-hander.