We are fortunate that after 9/11 the federal government worked hard to develop emergency response guidance and training for our nation. The NIMS (National Incident Management System) now provides the framework in which all of us should work to manage disasters like the one in Joplin. This system is comprehensive, and if followed, addresses many of the issues brought up in your discussion including transfer of command, handling of finances, delivery of services, and many many more. (The NIMS site has a lot of good info and case studies that can provide you with many answers to the questions you are asking.)
I would think Joplin, like many of us, has taken NIMS training and possibly even participated in exercises and workshops from training partners like TEEX. And because so many have had the unfortunate chance to implement the system during real disasters, there are many examples we all study and learn from.
Of course, it’s nothing compared to actually facing the real thing. But at least when a real disaster does hit, all the documents, command structure, programs, contacts, mutual aid agreements, ordinances, and other components you need should be available, familiar, and in place so you can better focus your efforts. So although it might appear there is a total loss of local management, there most likely is an EOC activated, and people are working in it as prescribed in NIMS. I would also expect that the Red Cross is on the scene. They usually play a significant role and act as a close partner when there has been this type of destruction and loss. (For people who want to help in disaster recovery, this is a great group in which to volunteer.)
And after the EOC finally closes and rebuilding begins, representatives from FEMA will move in. My emergency response experience has primarily been in disasters where there was no loss of life. Instead we had major destruction of infrastructure, and I found that FEMA was always there to provide valuable help and guidance in helping us with organizing our project list, obtaining cost estimates for repairs, and the management and financing of the reconstruction.
I do think the one aspect of a disaster that must be the most difficult is the loss of life. And I don’t think there is much preparation or training to really prepare you for facing that type of devastation.