Ok, what about colorectal and breast cancer mortality rates then

Same deal... Japan has a very low breast cancer rate meaning its mortality is lower with nothing to do with its healthcare system.

Focusing on the western world: essentially the goal is to catch Ca as early as possible because results are much better- for most sorts of cancer anyway. Obviously that's what screening is about.

Screening for breast cancer in the western world: 35% reduction in mortality from breast cancer in the 50-69 year age group. 50 is pretty young- there may still be dependent kids these days. 35% sounds pretty good but put another way it means that 1 life will be saved for every 500 women screened. I say "saved" but it would be more useful to say "enjoyed another 10 (20? 30?) quality years of life" if that's the case.

Colorectal: lots of arguments about screening here too. Bowel cancer is about 10% of invasive cancer and the majority doesn't present until the cancer is penetrating the bowel wall or has spread to other organs by which time outcomes aren't as good and treatment can be a lot nastier. Again an older population, 90% older than 50. Screening can reduce mortality by 10 to 15%. Quite a few countries have declared a screening program, most recently Ireland.

I believe that many US states do pretty well for screening, especially breast.