Basically, what has been shown with transferrin injections in mice is that this corrects several of the problems present in thalassemia.
Specifically, transferrin injections normalized labile plasma iron concentrations, increased hepcidin expression, normalized red blood cell survival and increased hemoglobin production; this treatment concomitantly decreased reticulocytosis, erythropoietin abundance and splenomegaly.
"... increased hepcidin expression" would allow the body to properly regulate iron absorption resulting in "normalized labile plasma iron concentrations". The body normally does not absorb more iron than it needs but in thalassemia this gets out of control, as hepcidin levels drop. Normalizing hepcidin levels would eliminate this excess iron absorption. Iron deposits would be cycled into red cell production but at a normal rate. The other side is a normalization of bone marrow activity, resulting in reduction or elimination of the production of defective red cells.
These changes would greatly reduce or eliminate the need for chelation, reduce the amount of bad red cells produced and reduce the problems associated with ineffective erythropoiesis and hemolysis. I can't say if this has any potential for increasing hemoglobin levels in beta zero but it would reduce the other problems, which are the main dangers of thalassemia.