Not sure what you are arguing here... if you are arguing that screening for cancer can be useful and saves lives, then I agree with you!
If you are arguing that a start up could have come up with a screening program for bowel cancer for example, then I don't agree with you for the stated reasons.
Also:
Prostate cancer screening is not recommended (http://www.cancer.org.au/File/PolicyPublications/Position_st...)
Breast cancer screening is not as useful as you would hope either. (http://dx.doi.org/10.1002%2F14651858.CD001877.pub4)
2000 women need to be screened for 10 years to save 1 life, with 200 initial false positives requiring biopsy. Also, I see lots of people diagnosed with breast cancer despite having mammograms.
Radical ways to do early detection are fine, but you have to prove that it works and that requires a lot of people for a lot of years and a lot of money.
Building a toilet with a bowel cancer screening kit built in is a form of behavior modification to improve uptake, and that is a great area for start ups to get involved in. pg was talking about something different however.