Doing this too often, however, steals valuable time away from the teacher that may reduce the quality of instruction for all the other students.
The teacher's mental and physical health is important, yes. But arguing that allowing retakes is a detriment to your own health, even though it is a benefit to the student, is a hard sell.
Case in point: my wife's family weathered two deaths in the same week. I left school on bereavement for one and had to extend my absence in the wake of the second death. We were in the middle of budgeting and my requests were not finalized.
My principal could certainly have disallowed an extension because I wasn't "proactive" and didn't have it done before the due date. Instead, I was given grace and I was able to submit a better report and request because of it.
Grace goes a long way.