[buckle8017]

Blood is tested for disease, but the false negative rate for each test is its own risk.

If you got blood from an addict living on the street engaging in prostitution and tested it, would you trust that blood?

I wouldn't.

[ctoa]

The bigger worry isn't really false negatives, modern PCR based testing is incredibly good. There is always risk but it's frankly extremely low. The bigger issue is that blood is pooled before testing to make that powerful testing economical. If you increase the rate at which you get (also possibly false) positives you risk having to throw out whole batches of pooled donations.

[buckle8017]

The false negative rate for HIV testing in newly infected people is actually pretty high, like 50% within the first few months high.

[ctoa]

No, it's not though. That's true for antibody tests commonly used for individuals because it's cheap. The window period for nucleic acid testing that is used for blood supply is very short. This test is similar to what's used to confirm a positive antibody test, but isn't used for individual testing because it is too expensive. Hence the pooling.