Despite being cursed with an endless string of horrible (for me - I'm sure some students did well) math classes from high school through college, the one thing I came away from with them was an appreciation of how much more intuitively you can learn mathematics if you don't use a calculator.

The problem with using slide rules as a replacement is that students would complain too much about learning something they won't ever use to ever get the deeper understanding that Cook talks about. Most young people who don't want a career in math, science, engineering, etc do not want a deep understanding of the principles - they want an A on the test. Unless you can use one of the external tools as a shortcut they won't be willing to put the effort into learning from it rather than using it.

Ban calculators, ban slide rules, ban everything except pencil and paper and hope that people gain some smidgen of understanding through sheer force of not having any other option.