White cell transplants arent used, it is questionable if they help and they are known to caused immune reactions in the host and bring pathogens (usually CMV) with them. If someone has an immune system so low they need white cells, THE LAST THING you want to do is introduce foreign material that due to its role has pathogens within it. But all of this aside, we already have treatments for low white cell counts....
When white cells get low, medicine is given to boost production. In blood cancers, bone marrow transplants and early precursor white cells can be transplanted (autologous stem cell transplant / allogeneic stem cell transplants). If a child needed white cells, as a baby they would receive them in the mothers milk and start making them too. From the sge of 4+ the risk of blood cancers arise and the solition of meds, bone marrow and white cell stem cell transplants is already in use. Harvesting red cells makes sense because we need red cells to live and time is a lidesaving issue, white cells just dont peform a similar role or function. In addition to all this, all cells even harvested and frozen have a short shelf life, red cells last around a month to 6 weeks only. So mothers breast milk cells only have a few weeks storage, a baby needing it in that time frame can simply get it from the milk anyway!