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Hot take: calculators are for experimental physics exams. In mathematics, they should not be required. If the exam is about multiplying five digit integers, then a calculator would defeat the purpose of the task. If the exam is about integration, then you can easily make sure that there will not be a lot of five digit integers to multiply.
Granted, some math classes are mostly to enable students to use calculators for their science classes. So sure, if the point is to learn to calculate logarithms with a calculator, you require a calculator -- no point in having students learn to use a slide rule. Likewise, for basic probability theory, a calculator will make a lot more practical applications accessible.
For my last two years of high school, Texas Instruments had somehow convinced my school board that their graphic calculators were great and educational. Our final tests featured tasks such as "determine the approximate root of this function with the graphical calculator". We did not cover a lot of math in these two years. I like to hope that graphical calculators are not a thing any more (a smartphone can do anything such a calculator can do, but much better), but if they still are, I would implore any school board deluded enough to think they would help teach math to at least make it a priority that the devices they mandate come with a decent programming language (LISP, Python, Haskell, Perl, whatever) so that kids do not have to waste two years programming in TI BASIC instead of paying attention to class.
Go to any office supply store near you. Are TI-83s still for sale?
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