From what I can tell, the gist of this question is that he has SCID and since the SCID child has basically no immune system (particularly because the lack of T-cell immunity) there is a higher chance of transfusion-associated graft versus host disease (TA-GVHD) so blood products have to be irradiated.

Here is a medscape reference with who requires irradiated RBCs due to increased risk of TA-GVHD for your perusing.

Irradiated blood destroys all nucleated cells, like in this case, we wouldn't want him to have foreign lymphocytes because it would cause GVHD for sure

Washed Blood eliminates plasma proteins, which is beneficial for patients with IgA deficiency for example