So far, there is not a suitable replacement for the oxygen carrying capacity of red blood cells. Artificial blood products tend to be either ineffective, or have bad side effects. Free hemoglobin solutions are a possibility, but are not available for clinical use.
Blood is needed to carry oxygen around the body. In severe blood loss cases, transfusions save lives. Blood also contains clotting factors, and we give plasma with massive transfusions to replenish those, and transfusions of platelets to aid in clotting as well.
Nothing "always" saves lives. Transfusions are one of those things that certainly can delay death, and allow the body to recover its own ability to make blood.
Whether there are long term implications of receiving someone else's DNA is immaterial if the recipient is dead from hemorrhage. Also, we routinely receive someone else's DNA during sex. Should we also refrain from that activity?
As an anesthesiologist, I've seen transfusions mean the difference between surviving and not surviving an operation.