It's worth noting that there is some disagreement in recent years whether large scale screening for breast cancer does more harm than good (see lengthy comment I made elsewhere), exactly because this information very often is not so vital and useful (many growths are not lethal, or would be detected soon enough anyway that it doesn't change outcomes), yet can be actively harmful (detection often leads to unnecessary treatments as it may be hard to discern lethal cancers from growths that will never pose a threat, and detection also causes stress and other issues).

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%...