Generals hate the light footprint approach. I was part of Project 404 in Laos, 69-71, talk about a light footprint. There were approximately 120 of us in Laos, half were Air Force mostly Ravens with AIRA, I was with ARMA. Our light footprint advising, supplying, logistics, commo, intel etc to the Royal Lao military helped them fight the North Vietnamese and Pathet Lao to a stalemate utilizing Lao troops and our air power from 1966-1973 when congress made us stop the bombing and ceded Laos to the commies.
Let me remind you of something more recent, Afghanistan. With just a few SF and paramilitary on the ground, our air power with the Northern Alliance troops, we were able to drive the Taliban out of Afghanistan in about a months time. Only after the Taliban had been driven out did we introduce a huge number of troops and those were for nation building.
Having said the above, what is needed for a light footprint to work is a sound indigenous force on the ground capable of at least standing their ground and better yet to be able to advance given enough air support and firepower from above. The Kurds have shown they can do this, but they do not want to get too far from their homeland. That means we have to wait on the Iraqi forces to be reconstituted and trained, supplied and organized. A quicker route would be to make nice with Assad, his military along with our air power has the ability to advance and drive ISIS out of Syria, possibly towards the Kurds. But would the Iraqi army be read for that third pincer from Baghdad? That is the question.