You've made the point about perfectly. All that I would add is the weaknesses of prostate antigen testing. Essentially it's just looking for immunological signs of prostate tissue in the blood as opposed to the prostate, a sign of cancer. Other things can cause this and the rate of false diagnoses is high enough that even investigating for prostate cancer is discouraged until men are of advanced age. Biopsies are more resource intensive, so most systems, universal or private, make an effort to frustrate people out of bothering.

Because of the lack of dialogue, there's not much being done for more reliable screening where women have mammograms and blood work that can detect it and confirm it.