As it is our tests only have about 1% false positive rate and tests being used in other parts of the world seem to be in the 3% range.
Please, don't have these crazy ideas if you don't know what you are talking about. You clearly don't.
A bad test isn't a substitute for a good test.
Simple example: I give you a bad test, determine you have cancer and cart you right into a weeks long immune system destroying chemotherapy treatment. And then we discover the test was junk.
Even worse: We test EVERYONE with this junk cancer test and give EVERYONE chemotherapy, blow up our hospitals, bankrupt the medical system and everyone ends-up half dead and immuno-compromised. Brilliant.
No, traceability and quality are supremely important, particularly when you are dealing with millions of potential patients.