A voice of reason.
If blood sampling becomes reasonably cheap, it may be of use in screening and monitoring.
If I get the 96% right, that concerns false-negative results, which you have elaborated on.
But there may also be false positives.
Which may be a great source of income to the odd cynic. Throw some screening at healthy patients, sponsor it if need be, then get a false positive, worry the patient out of his or her mind and then run expensive follow-up check like high-resolution MRT scans.
The patient will - at least in in the US - pay.
After all, as far as I can see, the results shout cancer without giving a location. Which in many cases would be like going to the police in New York and say, hej, I got terrible news. I know that there is a killer here in town. At least one.
But unless you have a location, this information has no value and the cops will shrug their shoulders.
And once you know the location, you do not need the blood test. So, the use of this method would be in screening unspecific symptoms or even healthy persons (depends on the price) and it all depends on the false-negative and the false positives...