The only question is what state interests are "critically important". The following is from the strategy section of the U.S. Navy's Qaudrennial Defense Review (it should be noted this is a draft; the final report is due today)
Finally, the changing international environment will continue to put pressure on the modern state system, and this will likely increase the frequency and severity of the challenges associated with chronically fragile states. The challenges posed by fragile states to American interests are legion, but two are most acute: such states are often catalysts for the growth of radicalism and extremism; and some states at risk are critically important to enduring American interests. Over
the course of the next several decades, instances of conflict are at least as likely to result from the problem of state weakness as from state strength.
Given the centrality of the problems associated with fragile states and the threats they represent to international order, U.S. forces will continue to perform missions ranging from stability and reconstruction operations, to developing the capability and capacity of security forces and their sustaining institutions, to combat advising alongside host nation security forces, and to the
provision of enabling support for international peacekeeping efforts. The responses fragile states demand extend well beyond the traditional domain of any single military service, or any particular U.S. Government agency or department.