That is precisely an argument that relies on a change in behavior in response to increased risk. I think you misunderstood the OP's argument.
That is a change in behavior to avoid risking injury to the hand and face! Can we agree on that?
You are arguing that overall injury is increased by using gloves because of the greater frequency and magnitude of punches, despite less severe injury per punch. But that is precisely the no seat belts argument too.
Gloves reduce the risk of injury to the hand and disfiguration of the face, just as seat belts reducing bodily injury in an accident. The argument then goes, seat belts encourage us to drive faster and increase the overall number of accidents, which in the end cause a greater amount of injury. That is the parallel with gloved punching. If we didn't have seat belts, we'd drive slower, because you'd get so messed up if you had an accident. That is the parallel with OP's no-gloves argument.
That argument seems plausible on the surface but as we know from seat belts, it has some problems which I've stated earlier.