HIV and T helper cells
Q1: Partially. T cells are important for the immune response through pathways other than cytokine release. Being activated by contact with another immune cell presenting their corresponding antigen, T cells proliferate and themselves activate their compatible B cell counterpart. These then produce antibodies specific to that antigen, the basis of the adaptive immune response (see figure below, from Wikipedia). The important part here is that this mechanism requires cell-to-cell contact, not simply cytokines. Without it, any pathogen for which memory B cells do not exist yet will not produce an adaptive immune response - and will persist if the infection is not cleared by the innate immune response.



Q2: I expect because merely injecting T cell cytokines would not be sufficient in order to replace the essential function of T cells. Aside from that, WYSIWYG's point about the general response is probably also true: the side effects would be horrendous.