How reliable does a test need to be in order to be used for screening?

A pro-screening friend posed this question — in response to my strong objections to mass screening.
To which I replied:
“It depends on the purpose, costs and the consequences.
Testing witches by tying weights to suspects’ feet and tossing them into ponds was a terrible idea. Yet at the time, many authorities decided it was a conclusive test — real witches didnt drown — and crucial to containing the scourge of witchcraft.
If I could offer some serious personal examples: When I was twelve, a servant in the house (yes that was common in India) was diagnosed with leprosy. Everyone in the family was immediately tested (with relatively crude, indirect tests) in a public hospital. I tested positive and was prescribed — and immediately started taking — a drug that would cure the disease but would eventually seriously damage my liver.
My mother, a cancer researcher not a medical doctor, wasn’t persuaded by the diagnosis. About a year later, after reading whatever she could find on the top, she took me to a specialized leprosy hospital. They redid the crude test and this time I tested negative. But since there was a prior diagnosis — and there was some abnormal scaling of skin — they performed a much more invasive, accurate test. They took out a large chunk of skin (about 5 mm deep) which they tested in a culture. After several weeks the culture showed there were no leprae bacteria. The drugs were immediately discontinued and later, when it was discovered I had developed an allergy to nylon socks, the scaling went away.
Accuracy here was crucial.
But what if the better test wasn’t available? Would I urge using the crude test to screen the population for leprosy. Absolutely not. But for people who had symptoms or circumstances that indicated the possibility of leprosy, yes. Even if misdiagnoses needlessly harmed their livers.
Another example: I am a sucker for all kinds of testing even when I know the accuracy of the test has not been tested (and is probably low). I have several gadgets to test blood oxygen saturation levels in my sleep (as an indication for apnea).  Im sure they are extremely dodgy. But they are harmless. Likewise, I know the 23andme genetic tests have no medical value to me. Yet I did them for sport — and got the “risk factors” for a thousand of my genes which I know are utterly unreliable.
The CDC has sensible criteria for testing for the flu (generally it recommends against). In my judgement those are pretty good ones for the corona virus as well.
And if you are really interested in the general issue of testing methods and tradeoffs look up the readings on that topic in my practical knowledge syllabus“