Should the US Try the "Theory of Second Best?"

Yes, we should. And it should be done immediately. Quick withdrawal from Afghanistan would force Karzai and his opium dealing warlords to govern their country by themselves. This would likely result in the collapse of the corrupt government that calls Kabul its home. Sounds vicious, doesn't it? It would paint a far rosier picture than would staying our current course. Peter Leeson and Claudia Williamson argue in a paper that, 

Many predatory governments do more to damage their citizens’ welfare than to enhance it. In light of this, we show that conditional on failure to satisfy a key institutional condition required for ideal political governance—constrained politics—citizens’ welfare is maximized by departing from the other conditions required for this form of governance: state-supplied law and courts, state-supplied police, and state-supplied public goods. Since departing from these conditions produces anarchy and fulfilling them when government is unconstrained producers predatory political governance, anarchy is a second best.