I don't necessarily agree with this. Programs are not designed to be readable, they are designed to solve a problem. The first goal is to get the correct program, and only after, it is important to make the code readable. A readable code that doesn't work is not worth much.
As a former student, I think automatically graded assignment are very nice because they force you to have a programmer mindset (the smallest error / typo will make your code fail).
If you want to grade also the organization of code, fine, but I think the first one is more valuable (how to organize code properly is not learned at school anyway, it is learned by months / years of practice).