None of you understand the CDC guidance for the new tests. There is no quick test that can differentiate anything. Think of it more like a pregnancy test, it comes back positive or negative and you have a large range of error, typically towards the positive (eg. if you have a hormone imbalance, you will test false positive, but that is acceptable given a false negative whether you are pregnant is worse)
Detailed analysis should be done and is done for any other quick test (eg. HIV or something simple like a cough or a lead test will get you sent to a lab for a blood test). But due to the expected volume, blood/microscopy tests (1-3 day for results) weren't considered feasible, so CDC approved doing quick tests without blood or microscopy tests to back them up. Due to my position in a local hospital (yes, that's where I work), I always got priority blood tests to back up positive quick tests, they always came back negative even though I've tested positive with the PCR test 3 times now. This is partially what is currently driving a 30-40% refusal rate for the vaccine amongst healthcare workers.
Yes, prior tests would not detect flu, they would only detect ANY coronavirus. The new tests can test for ANY flu AND ANY coronavirus. I think there is a third one on the new tests, but I'm too lazy to look it up. At that point, the doctor should send you for a blood test if they went with pre-COVID protocols. The CDC just want to make testing for flu/COVID faster by doing it one test and then telling you to isolate rather than doing 2 or 3 individual tests.
CDC doesn't revoke anything in regards testing, they just won't reimburse you if you don't use their new standards, so hospitals are on the hook for any tests and resulting care. As with everything fast/accurate/cheap, choose two. They chose fast and cheap.