This turned out to be false, but being able to do mental arithmetic is still an extremely valuable skill. The usability of your pocket calculator is really bad in comparison, and what the mental arithmetic gives you is a general automatic numeracy where you can ballpark the answer to numerical problems much faster than using a tool.

This becomes a qualitative difference because you'll do more of those mental checks as a matter of course that you would never pull out a calculator for. Kind of like how git made merges so painless that they're now a standard part of most people's development flow. That's the kind of qualitative impact that mental arithmetic can give you.

I admit that this is a point that's difficult to get across, and schools generally don't do a great job of it...