Never in high school was a calculator allowed on any math tests. All problems were written to be solvable without a calculator, and they were plenty challenging. And this way, the students were pretty confident when they were going astray on an answer, since most everything wound up being a whole number, basic fraction, or one of the more common irrationals. I graduated High School is 2001 from a public school as well.
Whats more important is that they taught is math, not how to use a calculator. How to use a calculator changes with the calculator, and isn't a particularly valuable skill to learn compared to the fundamentals of calculus and the other higher math. Yes, I almost never do math anymore by hand, I write a program for it, but learning all those fundamental rules about the quadratic equation, even those weird trig substitution formulas come in handy once in a while when solving a weird problem.
Calculators aren't necessary in high school mathematics, and should not be used.
Now for chemistry and physics I can't see no calculator simply because the numbers are so unwieldy most of the time, but I think there is a way to write a test that does not require a calculator.