Important Circumcision Question (ICQ)

I’d like to briefly pose the following ICQ:

One of the primary non-religious justifications for the practice of circumcision is that it has health benefits. Circumcised men are less likely to get some STDs than non-circumcised men. But if we found that cutting off a person’s nose reduced the risk of their getting the flu, would this serve as a justification for cutting off children’s noses? Why would health justify the one procedure but not the other?

This is far from a point original to myself. Many opponents of circumcision ask this question also. But I have not found a satisfactory answer yet, and I would like one.