How bad would it be if you injected something that killed all CD4 T-cells?
Like how long would it take until new ones formed and how vulnerable would you be until that happened?
That's in essence what HIV does. You'd give the patient a quicker onset of AIDS. Perhaps if you eradicate the rest of the HIV and keep the patient stable in some other way this could work... but I think this sort of scorched earth method isn't/wouldn't be as attractive as a targeted cure due to the period you'd have full blown AIDS.