Look at it another way
Giving someone blood is the equivalent of giving then a dangerous drug and whatever may be in your blood may not be compatible with a very sick person
When blood goes back to the laboratory it is tested for ABO group Rhesus group, HIV, Hep B, and various sexually transmitted diseases

You will be asked if you have any infections or if you are taking any medication because those things can make a sick person a lot worse
The reason is that hospitals do not test for infection or cancer or any of the millions of illnesses that you could be carrying
One of the good things about having a Blood Transfusion service in this country which requires a voluntary contribution is that people are more likely to be truthful
In countries where they pay people for giving blood you then have the risk of a drug addict giving blood for money and not admitting to using drugs or needles which all carry risks of Hep B and HIV as well as goodness knows how many more infections
but there is also innocent risk in that you may not know that the virus you are carrying tomorrow may well be in your blood today.
BTS don't test for that
If you went to your GP and said I feel ill they would do a blood picture to see what is going on and white cells may be raised but that isn't done in BTS They just make sure you are not anaemic
It would be almost an impossible task to check everybody for any eventuality and even if they could it would cost a fortune