That is poor teaching. My kids were almost always allowed calculators (always after the age of 8 or 9) and they can do all that and a lot more (my older daughter is an electronics engineer, in R & D).

For one thing you do not need to do much arithmetic to do algebra, for another estimating and getting a feel for numbers is not the same skill as learning a bunch of arithmetic techniques. No one is going to do long division while shopping.

Um... there's always exceptions.

I can keep enough digits in my working memory to do long division in the grocery aisle.

I also compulsively factor numbers on license plates..