One "essential learning" in first grade math is that students need to understand addition and subtraction. If a student takes a test on adding and fails it, should you allow a redo? In the primary grades, we tend to understand that the student needs to master the content.
In later grades, the answer is often that a student should not be allowed a retake because he should have studied the first time. We have the impression that giving a student a lower grade will hold the student accountable. In many ways, the low grade lets the student off the hook. The student gets a low grade and they are done. We also like to use future teachers as the reason we can't allow them to do a retake. We have to teach them they won't get good instructional practices in the future by not giving them good instructional practices now. Not allowing redoes and retakes sends the message that the timing of the learning is more important than the content.
If a first grade teacher took the approach that learning responsibility is more important than addition, think of the impact that would have on this student as he moves into 2nd grade and throughout the rest of his education. Which lesson will be more important in 2nd grade, knowing how to add or the fact that the student (supposedly) learned to be more responsible by not being allowed to continue to assess his math facts?
Study habits are important. Rather than using punitive grading to "teach that kid a lesson" maybe we need to take time and teach study habits. When they fail, help the student create a “retake plan.” Require them to re-take and redo. The retake, by it's very nature, will be more time intensive.
We want students to be responsible. However, that lesson should not be at the cost of mastering the content. Keep a separate grade for responsibility and make studying the first time a more desirable option.