Any time someone uses the word "control" in this sort of context there has to be a healthy appreciation for the extent to which some things are simply not controlled. I'm sure the usual suspects have a relationship with the extremists, and may have some influence, but the extent to which they exercise "control" is quite debatable. It's easy for outsiders to say, for example... we cannot control x, but y controls x and we can influence y, so all we have to do to get rid of x is to put enough pressure on y. It rarely works so simply in the real world, largely because "control" is often variable and incomplete.
I wouldn't want to lump the ruling elites of the Muslim world, or even the Muslim world in any sense, into one basket. Much of the Muslim world has no oil and no economic influence. Parts of that world have oil and influence... realistically those governments exist in symbiosis with the modern world and the need on either side is going nowhere. Different parts of that world need to be dealt with in different ways.
I doubt that most Congressfolks know or care much about it. Until the US presence in Afghanistan is reduced to a level that no longer requires land supply routes it's not likely that the US will shake things up with Pakistan in any lasting way.
Once the US no longer requires Pakistani cooperation to supply forces in Afghanistan, it would be theoretically possible to stop all support to the Pakistani government. Of course if that started us on a road that ends up leading to an extremist takeover we might end up wondering whether that was the right decision...
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