Situation: person has an almost undetectable cancer. They see a doctor, no cancer detected, later that week they are shot by police at a routine road stop.

We get in our time machine, go back a week and a bit, and supply the doctor with a better detection kit.

Situation 2: person has an almost undetectable cancer. They see a doctor who refers them to a specialist, cancer detected, another notch on the cancer tally board. Later that week they are shot by police at a routine road stop.

Nothing has changed except in the second case there’s another cancer detected. The person is still dead from non-cancer causes, just in one scenario they died as a haver-of-cancer and in the other they didn’t.

Better/earlier detection will necessarily lead to a decrease in cancers that are never detected (which I interpret as an increase in cancers detected before mortality from other causes), otherwise it’s not better/earlier detection.