> An "A" in calculus should mean that you can do calculus and that evaluation should be independent of your own strengths

If you can't do calculus, extra time is not going to help you. Its not like an extra 30 minutes in a closed room environment is going to let you rederrive calculus from first principles.

The theory behind these accomedations is that certain people are disadvantaged in ways that have nothing to do with the thing being evaluated.

The least controversial version would be someone that is blind gets a braile version of the test (or someone to read it to them, etc). Sure you can say that without the accomadations the blind student cannot do calculus like the other students can, but you are really just testing if they can see the question not if they "know" calculus. The point of the test is to test their ability at calculus not to test if their eyes work.

The braille example you give makes absolutely perfect sense. The blind student is being evaluated same as the other students and the accommodation given to the blind student (a Braille version of the test) would be of no use to the other students.

But extra test time is fundamentally different, as it would be of value to anyone taking the test.

If getting the problems in Braille helps the student demonstrate their ability to do Calculus, we give them the test in Braille. If getting 30 minutes of extra time helps all students demonstrate their ability to do calculus, why don't we just give it to all students then?