Of course it would be daunting to solve the conflicts the Islamic State feeds on, but that shouldn't be the mission in the first place.
Stephen Biddle and Jacob Shapiro's recent Atlantic article, "America Can't Do Much About ISIS," advocated containing the Islamic State and questioned America's ability to destroy the group. The first problem with this analysis is how the authors define "destroy ISIS." They compare the amorphous fight against al-Qaeda with the one against ISIS, discussing how to get at the roots of its terrorist ideology and fix the ungoverned space that provides its sanctuary. This leads them repeatedly to conflate destroying ISIS in its current form as a quasi-state with the monumental task of resolving the Syrian Civil War and the Sunni-Shia split in Iraq. To the contrary, if the mission is properly defined, America can destroy ISIS, and must.
Defeating ISIS-as-state is not dependent upon solving Syria as a social, historical, cultural, religious, and governance project, let alone doing the same with Iraq. ISIS feeds on the conflicts in both countries and makes the situation in both worse. But it is possible to defeat ISIS as a "state" and as a military-economic "power" -- that is, deal with the truly threatening part -- without having to solve the Syrian and Iraqi crises or eliminate ISIS as a set of terrorist cells or source of ideological inspiration. Of course, even if ISIS is destroyed as a state, we would still have the Syrian Civil War and Iraqi disunity, but we have all that now, along with ISIS, which presents its own challenges to the region and the West.
Normally, if one opts not to ignore a foreign-policy problem, the two choices are: Fix it (which in ISIS's case would mean defeat and destroy it, per America's official policy), or contain it. The choice is made based on an analysis of the likely costs and risks of eliminating the problem versus those of living with it, as well as the impact of one's decision on broader concerns. From both points of view, Biddle and Shapiro's arguments are flawed...