Tests cost money. They have blood enough to allow them to discriminate. If they were lacking, they will be less picky: in a catastrophic event they call for blood donors and they rely on tests, risking a detection window.
But under normal conditions, letting only the best candidates donate is the most efficient way.
Generally, because they're discriminatory. It's like how racial profiling in law enforcement can be a heuristic that can work. Though, in the case of blood donations, it seems that tests aren't accurate enough to be able to rely solely on them. Also, being discriminated against on being able to donate blood is not as big of a deal. Though in some places with public health systems, stuff like getting a surgery may somewhat depend on you and family/friends donating a certain amount of blood.
should test? As in test the blood? Or test the hypothesis?
if the latter I'm not sure it's enough of a stretch to say unprotected, hi-risk, promiscuity is a risk factor for blood borne illness like HIV? (Such that we need to research it separately)
But under normal conditions, letting only the best candidates donate is the most efficient way.