Interesting question with a few different angles that it could be approached from. I think military being used for things like disaster management is going to grow due the reasons that Ths stated: They are organised hands under a central command.
Firstly: I think that the military is well suited to providing logistical, transport, and medical support to disaster area's as they have very specialised equipment and training that is designed to bring materials and people into inaccessible areas during war time. I don;t think that they should be providing any guns (see second point). Often during natural disasters transport infrastructure is damaged or destroyed and the military becomes the main agency that can move supplies to these places. So for transport and logistics support I think we will see more and more military involvement as it makes sense to have the dual roles as its just more efficient. Where there is big military commitment to distant wars one would run into big problems though if disasters happen and the rescue team is away so to speak. This is why its best not to have too big a reliance on the military as it may limit them in providing their primary function, or leave you in the lurch should they be committed elsewhere to a conflict. Military medics are also great in disaster areas as they are trained to dispense aid and set up field hospitals in potentially hazardous areas. They would go in with water purification equipment as an obvious example while a normal hospital would not have that kind of thing off hand.
Secondly I thought I would just mention the policing function of soldiers. Soldiers are trained essentially to kill. Police are trained very very differently. Their roles, mindsets, training, and objectives tend to differ and that is why military people seldom make good police forces. Where possible I think police should be used to control areas that are having disasters. There is overwhelming evidence that during natural disasters there is an almost immediate break down in law and order that gets progressively worse the longer the effects of the disaster roll on. Looters started looting jewelry stores while the waves where rolling in for the Asian tsunami, and people where shooting at cops after Katrina. Think along those lines. This is where it is tempting to use the army guns to restore control but a better solution is to converge riot police and normal police from other areas of the country into the disaster zone to maintain order. If manpower is really that short then army MP's should be used as support but in conjunction with normal police with the police clearly dictating the rules and policies. This way its easier to disengage the Army personal when the situation improves and keep the rule of law in the hands of those sworn to defend it (the police).
Army people are not sworn to maintain law and order, they are sworn to defend the national integrity of their country and to kill where they are told to. This is why the roles are normally kept seperate.
Disaster management is a field that has come very far in a very short space of time. I have been in disaster management centers for big corporates like BHP Billiton. They have board rooms and offices set up with maps of different mines, locations, lists of closest aid to each mine that could suffer a disaster, lists of agencies to contact for each place, etc. They have templates for every conceivable type of disaster set up so that people don't have to think "what do we do now that this explosion happened deep in a Columbian mine", they already know. Just follow the steps listed on the template. They have satalite TV links to similar board rooms all over the world so that the closest one can co-ordinate and the rest can be kept up to date with the efforts. Its really incredibly to see just how fast they can react to a situation. People like the UN and red cross, and most governments, have some of the best professionals in this field and have teams dedicated to co-ordinating relief efforts of all kinds. They should thus hopefully have resources made available to them from normal civilian channels that could handle most disasters but also be prepared to accept and utilize other forms of aid, including military aid.
Interesting aside: Did you know that it is recommended that each family in the world have an emergency 72 hour kit of food, water, and emergency equipment as well as crucial identification documents. The 72 hours is because that is the worst case time it will take for international aid to reach any part of our planet (baring political obstruction as was seen in China recently).