Hamilton was an old fashioned imperialist (e.g. wanted the U.S. to conquer territory like other “great nations”) but that has nothing to do with the Modern Wilsonian, and neo-con, concept of spreading democracy. The primary motivation for Hamilton was old fashioned power politics not bringing “’representative government” to the world.
What do you think the primary motivation was for establishing representative government in Iraq?
Think: what countries border Iran?
Turkey - a NATO member. Azerbaijan, a US ally. Armenia, another US ally despite the conflict with Azerbaijan. Turkmenistan -a US ally with US airbases. Afghanistan - a US ally with NATO presence. Pakistan - a US ally. Across the Gulf of Oman is Oman, the UAE and Qatar - all US allies.
Finally, Iraq - a US ally with substantial US military presence.
Iran is completely encircled by US power.
Humanitarian interests and US national interests are usually identical - Hamiltonian conservatives knew, and today's conservatives also know, that the US does well by doing good.
Wilson - a Jeffersonian radical and Confederate sympathizer - has nothing at all to do with current US policy in the Middle East.