There are other rich nations that treat breast cancers with chemo/radiation ~25% as often as American doctors, and get the same overall breast cancer mortality rate.

That is extremely strong evidence that American doctors are applying a painful & damaging treatment far more often than can be rationally justified.

Still, there's no way you can know in a particular case if the cancer will respond to chemotherapy or not.

And how are you measuring mortality?

In some cases, no; in some cases, yes.

By the number of women who actually die of breast cancer.

Suppose, normalized for population size, 1000 women of a certain age die of breast cancer in both country A and country B. In country A, 5000 women are treated with chemo. In country B, 20000 women are treated with chemo.

Which country has the more competent doctors? I think the answer is obvious.

Hint: The USA is not country A.

The answer isn't obvious at all. What if in country B the average woman with breast cancer lives an additional five years? What if breast cancer is simply more prevalent in country B?

You're trying to oversimplify something that isn't simple.

By the way, exactly what country are you talking about here?