Since it is possible to take a patient's cells and generate a very large number of immune cells, far more than the patient would ever have normally, and since it's possible to make some alterations to immune cells to make them more effective, why not do this? It's probably the case that even generally healthy older people would benefit from a regular infusion of large numbers of their own immune cells, or even donor cells, given the way in which the immune system declines with age, but under present medical regulation you'll only ever see it deployed as a treatment for late stage disease:
[Researchers] have successfully infused large numbers of donor T-cells specific for a key anti-leukemic antigen to prolong survival in high-risk and relapsed leukemia patients after stem cell transplantation. [T-cells were] taken from a donor, programmed in the lab to recognize the Wilm's Tumor Antigen 1 (WT1) and kill leukemia cells, grown in large numbers, and then infused into patients to promote anti-leukemic activity. The WT1 protein is overexpressed in leukemias and is in part responsible for why the cells have become leukemic.
All of the patients [received] adoptively transferred infusions of billions of enhanced CD8 cytotoxic T-cell clones. They were considered at high risk of death because they had already relapsed and/or had a poor prognosis due to unfavorable characteristics of their leukemia.
Four of the 11 patients in the trial received infusions of T-cells that targeted WT1 and were generated in the presence of IL-21. One had detectable relapsed disease and entered complete remission shortly after the T-cells were infused. All four survived after T-cell therapy without relapse for more than 30 months without suffering graft-vs.-host-disease and required no additional anti-leukemic treatment, according to the study.
Among the seven patients who received infused T-cells generated without the presence of IL-21, two showed direct evidence of anti-leukemic activity, including one patient with advanced progressive disease who had a temporary response.