"or for simple quizzes that can be graded automatically"

I remember at least one test like that when I was at school (in the early 90s). There was a special printed form with places where you would mark your answers (to multiple-choice questions) by filling in rectangles with a pencil. These were read by computer.

Of course, this would be even easier to implement now. No need for students to carry computers or a fancy SPA to administer the test.

(Assuming you don't need adaptive testing.)