Flocks of spontaneous volunteers can become "the disaster within the disaster." They can hinder efforts by first responders. They can be injured. Appearing on site in large numbers without their own food and shelter, they drain resources needed for the afflicted. Therefore, disaster response agencies train with exercises in managing spontaneous volunteers. This intensified after 9/11 and Hurricane Katrina. In point of fact, earlier documentation suggests a lack of a problem.

Reports from the 1960s and 1970s indicate that volunteers seemed to know what they were doing. They were largely appreciated by the victims and welcomed by the official responders. The University of Delaware maintains a huge repository of research and reporting on disasters. It was inherited from Ohio State University and it goes back to the 1960s. See the Disaster Research Center here:
http://www.udel.edu/DRC/

Contrasted with the response to Hurricane Betsy, the sociology of Hurricane Katrina points to a shift in dynamics. The federal government was surprisingly quick to respond in the first case and disappointingly slow in the second. Both were motivated by power politics. President Lyndon Johnson sought to mollify Dixiecrats who opposed his policies and held leadership positions in Congress. President Bush's FEMA had no analogous incentives.

Also, perhaps more deeply, the emergency preparedness officials of the 1960s inherited the orientations of World War Two as applied to a Cold War that was heating up. By the year 2000, decision makers and leaders approaching their 40s and 50s had no similar experiences. The broad narrative is that in World War Two, the government looked to the people to buy war stamps and war bonds, to contribute scrap, to plant gardens, etc. Much of that, perhaps all of it, was just propaganda, as no real privations faced the American people as a result of the war. Nonetheless, by 2000, the mainstream assumptions within the population centered on what the government would do for them -- and they had 40 years of experience with school lunches, superhighways, a space exploration program, and much more. Each hurricane brought evermore federal largess.

If you enter "Managing Spontaneous Volunteers" in your search engines you will find many resources from American websites. You also will find a few from Australia and New Zealand. Other people in other places and are less willing to help their neighbors in times of distress.