My wife uses much the same technique. What I've found interesting is that the students who need the points the least are typically the ones who will do the work to get the points back. IOW, the student who fails with a 60 typically won't turn in the corrected test, but the student with a 95 will.
My good students almost always take advantage of the “freebie.” But a surprising number of my other students do too. I do it for another reason, too. Only 20% of this class grade is computed by test grades. It’s a hands-on class where there must be a lot of presentations. I’ve found that if students start out with a low test grade that they get discouraged thinking that they will make a low grade in the class no matter what they do. I don’t want that, so it helps all of us if they have the opportunity to do reasonably well on the first test.