The obvious answer as to why this is not the case, of course, is the fact that President Snow (Donald Sutherland) is an evil, ruthless, tyrannical bastard.
Even so, would it not boost his approval ratings among the lesser privileged states if he actually showed them proof that he gave a damn and used his resources for good for once?
I mean, given their seemingly unlimited wealth and the unfathomable things that scientific progress has allowed for them (instant injury healing cream, for instance), I do not think it would take much effort to, say, end world hunger with some sort of microwave that zaps up a whole feast in seconds or ensure every family has shelter with fireproof houses.