That's too application focused. The primary value of arithmetic is that it forces you to exercise parts of your mind in a way which would otherwise be difficult.

The same can be said of general mathematics, and literary analysis, etc.

Hum, basic arithmetics is mechanical repetition. There may be some benefit to the brain in doing it, but I'm doubting it until I get evidence.

The main benefit is that knowing arithmetics well makes higher mathematics easier to learn. That's because one won't get distracted doing calculations. That's still true on the calculator era, just a bit less so, thus I do think it's important to learn arithmetics... It just the "it improves your brain" that I find highly suspect.

That doesn't mean it isn't a valuable skill. Mental arithmetic can also improve other brain skills.

No? As an Asian student I have seen countless people try to push their children to exercise arithmetic skills because they believe that does good to their brains. However, it only misleads children to hate "math" and sometimes even their lives based on this the most important subject again and again. Moreover, children would wholly waste their exercised brain on the ruined confidence because some of them just cannot "recite" the patterns well among questions in tests, because you're required to answer too much questions during too short time, which means if you cannot recite the solution patterns from textbook and calculate the answers right at first time, you barely have no chance to try it again. Even those who did excellently in those high-school tests will face another crash at the beginning of university, because the "real math" no matter cares your arithmetic skills, but your abstract thinking and the feeling to grab and deduct rules from axiom. After all, except those real geniuses can conquer these two very different requirements and continuously get payback from that, I don't see any benefits from focusing on arithmetic with so high-strength training.

To be fair though, that's the math version of "I don't need to know JavaScript at all because I will always have jQuery." Technically accurate but lazy.

Javascript or 9x14 is not the kind of knowledge that's valuable for its own sake. http://unreasonable.org/Feynman_and_the_map_of_the_cat