The error you make here is to analyze the "opinions of Pakistanis" from a much more detailed perspective than they do themselves. Like I said, for the average Pakistani an Islamic system means one that provides "Justice and Equality"
This is actually a very crucial point which needs to be investigated and elaborated upon further in Islamic communities.
I think your observation is spot on. I too am fairly certain that the majority of Pakistanis and many other Muslims who want Sharia to be instituted (ranging from Africa to even certain areas of the UK and other parts of the west) do so without truly understanding it's complexity; rather they blindly entrust their faith system to provide a fantastically benevolent system of law and order which is supposed to be far superior to the corrupt and unjust one that currently exists. This is a far cry from how the western world perceives this issue. They somehow feel that these demands are made by entire masses of Koran memorizing Muslims who walk around with beards and bomb laden vests.
Nonetheless, this is a faulty notion propagated by the emotions and needs of the currently beleaguered Islamic societies. It is fairly obvious that corruption and injustice are actually byproducts of incompetence, apathy, lack of proper social development and poor/misplaced social values which cannot be fixed by merely solidifying/enforcing faith on a mass scale (I am aware that some may disagree with me strongly on this, but please hear me out). I agree that by pushing faith at the forefront, there is a short term feeling of solidarity and progress, but eventually that too fades away as the core pathology rears it's ugly head. This trend can be seen in many north African states (including Egypt), Afghanistan and Iran.
Now mind you, this phenomenon is in no ways limited to the Muslim world. Islam is merely the current hot topic. The same effect can be recreated by substituting religion with a radical nationalist/political ideology as seen in many nations of South America, the ex Soviet Union, India (1947-1991) and Cuba to name a few.
But coming back to the topic at hand, the point I'm trying to make is that People in the Islamic world who are trying to stabilize their societies need to be shown that the answer to their problems isn't religion, but good policy and governance that is first and foremost answerable to the immediate needs of its people. In fact, it is far better to keep religion in the private sphere and not let it metastasize into the efforts required to improve the conditions of their states.
Now I am fully aware that even initiating such a discussion will elicit a highly negative response. People will vociferously rebuke such ideas because they will be seen as an affront to core beliefs and values and/or outright blasphemy. But I really feel that this is a very important dialogue that needs to be started in the Islamic world (what ever that is).