Probably stating the obvious here, but the reason they stopped the practice was because people did such studies. If bloodletting worked on any common injuries

Probably stating the obvious here, but the reason they stopped the practice was because people did such studies. If bloodletting worked on any common injuries or illnesses, we'd still be using it for those cases. Even then, we'd probably have tried to find medication that produced the same benefit to try to avoid the infection risks.