I don't know any "did early detection which lead to unnecessary chemo" stories..
I know people who died due to the lack of early detection.
I also know people who survived due to accidental pre-symptomatic detection because of unrelated ER scans where they'd have been in stage 4 before having any symptoms.
So more screenings for more types of cancer are absolutely needed. It's more treatable early, and you will have better outcomes.
Patients might worry about lab results is not a good reason not to have early detection. Patients can self select if they are so sensitive.