I would be fine with a pretty high false positive rate when you are getting such vital and useful information.
You also need to keep in mind that that it is very possible the false positive rate will be per test, in which case with regular screening 1% quickly turns to 10%...
Cancer treatment is highly lucrative, though.
It should be noted that at the moment, the researchers are still working on determining which of the 8 cancers is present in the case of a positive result.
Screening tests are about cheaply directing further testing.
Early screening will occasionally save some. The question is whether it will save enough to make up for that harm if we increase the frequency of testing.