you'd be up to your ears in false positives, which can often be worse. screening is hard.
Large scale testing is highly dicey and requires careful consideration because it often takes very low risks from false positives to outweigh the benefits.
When a true positive is rare, the false positives can easily swamp them. E.g. one Canadian paper claims a glucose test for diabetes gives a false positive rate 6 times higher than true positive in the general population [1] (the numbers will of course be much better in a group where risk factors are present).
A challenge is that becoming confident of the ratio is difficult. What do you count? Routine mammography has been scaled back some places because even miniscule false positive rates seemed to rack up enough downsides alongside surprisingly low benefits (you caught things earlier, but the difference turns out to have less impact on survival rates than you might think) when the true positive rate is also tiny.
The end result is that the candidate pool for large scale screening programs where we can be confident of a net benefit is surprisingly small, and it may well be we'll see further declines in use of large scale screening rather than increases, as improved treatment often further cuts into the net benefit of early detection.