I do give makeup exams, but subject to the following constraints:
1. I determine when the makeup is given, not the student. I give them plenty of advance notice so they can adjust their schedule accordingly.
2. A student gets one chance. If they miss the makeup exam date, too bad.
3. I determine when the makeup is given, not the student. That means I don't negotiate on the date.
3. My makeup exams are always harder than the original exam.
There's nothing wrong with that policy.