If you're curious you don't need to just wonder. There is of course a lot of research looking into exactly these questions. Here is a summary by the FDA:

https://www.fda.gov/medical-devices/coronavirus-covid-19-and...

This article seems to be about the tests not detecting early enough. Which could be a test sensitivity issue or even could be a shift in how the new strains interact with our immune systems.

I recently had COVID and found that the test showed a faint bar right after my first sign of symptoms. Because I had plenty of tests, I continuously tested the 4 in my household as symptoms progressed and receded.

Although the visibility of the bar can't reliably be used to gauge level of infection, it did roughly track with my whole family's symptom severity and was confirmed with a PCR test.

After months of using these tests, we never got a positive either until this point.

These were the orange, made in China tests that the federal government is sending out for free.

So while they may not signal early enough to do much good, they certainly seemed to work in our small example.