The aims you state are indeed the putative aims of American policy, but (as you say) the democracy angle is a most unlikely one, and, as Starvid says elsewhere on this thread, the "terrorists" are safe in the tribal territories of Pakistan (and, indeed, in adjoining mountainous territory in Afghanistan). In my view this is thin cover for a policy of maintaining influence in Central Asia and the Middle East (and energy resources), policy which considers Afghanistan as the frontier to hold, right up against China.