As we know, in case of severe bleeding, positive feedback mechanism of the heart may lead to death; and transferring blood in conventional way takes a long time. So why don't we think to a simultaneous way for it?
1. You have to type and crossmatch blood before transfusion. Stored donor blood already is typed, so using it expedites that process. Ringer's lactate can be infused to maintain volume while you are typing the patient's blood and cross-matching.Stored blood also has been tested for HIV, hepatitis, etc. Wouldn't your live donor need to be tested too?
2. Direct patient-to-patient transfusion will not flow faster than stored blood transfusion, in fact often is slower as you have to protect the donor as well as the patient and you can't use a gravity-fed controlled flow..
The whole idea is to transfer only those components that are really needed (plasma, erythrocytes or thrombocytes). Nowadays you can skip crossmatch in 90% of cases if you have typed erythrocytes in store and the patient doesn't have antibodies.