Saddam Hussien (dead),
the electrical system non-functional,
roads and bridges unable to support mobility,
military officers demoralized or defecting,
air defense unable to interfere with US operations
Let's use this as an example (and I read '91 here):

Two approaches to air war:
'True' strategic air war with the intent to break the enemy government('s will to resist) directly with air power
and
operational air war in support of other arms; usually land support of a land campaign, rarely (Pacific War) primarily support of naval warfare. This may include bombing industries if those industries supply the OPFOR.


Saddam Hussein was caught in a miscalculation.
His withdrawal (the mission to be accomplished under UN mandate) would almost certainly follow if he understood his mistake. Offering him a way out that saves his face would likely reduce his resistance once he grasps the situation (and hurry the process up).


So what needed to be done? He needed to be convinced that the situation is serious. Air power eventually achieved this when he ordered a withdrawal (ground offensive was accelerated to interfere with the withdrawal iirc).

It did actually not take much to convince him that the coalition was serious. Diplomats could have paved him a nice way out of the mess and air power could have demonstrated political resolution with actual attacks. Those actual attacks could have been directed against his counter-strike capabilities in order to minimise the mess; attack aircraft airbases, SCUDs (the latter did eventually fail, of course), suppress long-range artillery (longer range than the ubiquitous D-30's).
This would have required some self-support of air power in form of the strike package support; SEAD, AEW, ECM...
The bombing of barracks, bridges, palaces, electrical nodes, tanks and bunkers was not strategically necessary (the CAS at Khafij was tactically useful, though).


Now another version; air power in support of decisive land operations.
The scenario is roughly the same, but the decision is expected to lay in the hands of the ground forces (assumption: Hussein is too stubborn to yield to air power alone.
Air power softens up and deceives in order to prepare for a decisive land campaign advance: A near-encirclement of the occupation forces in Kuwait would almost certainly force Hussein to accept the need to withdraw. Alternatively, the encirclement could be completed in a more Clausewitzian approach of disarmament.


It should be obvious in both cases that I'm not intent on destroying a card house with some smart moves; I'm intent on defeating the will.
I look at personal preferences and assume somewhat purposeful decision-making within the limits of typical psychological malfunctions (such as cognitive dissonance or problematic group dynamics).
An enemy head of state only needs to be attacked if it itself is the problem or if by assumption a successor would be more inclined to bow to our demands. Aggressor politicians deserve a high explosive event, but killing them makes it damn hard to negotiate an armistice with them in the following days and weeks.

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The 2nd kind of air warfare (in support of a decisive surface campaign) isn't truly strategic in my opinion, but rather a support campaign that works through the economy/infrastructure (WW2 examples). It's working only very directly towards victory:
Air power succeeds to pave the way for its exploits (SEAD, air superiority fight), air power affects the enemy at home (supply flow to OPFOR reduced), blue surface forces defeat red forces in battle more easily, red government accepts that it was overpowered militarily, its will is broken.
That's often way too indirect because more direct, more elegant, approaches are available.