We don’t routinely test for flu because , on the whole, you are far too unwell to go out and about anyway, and flu testing is somewhat problematic and far less reliable than the covid test.
you are far more likely to get a false negative with a flu test.
The point with all illnesses is it’s not how well you feel , it’s what effect going into the population will have.
Most kids with chickenpox don’t feel too bad before their spots crust over but should you take a kid who feels well to a child play area with chickenpox when they feel ok?
Would you want the person cooking your food in a restaurant turning up to work having taken Imodium to control their infectious diarrhoea?
Would you want someone in childcare changing your babies nappy when , although they feel ok , they have impetigo?
It’s not illegal to do any of these things , but it doesn’t make it right .