My (outsider's) impression of most private militias is that they often structure around people who are itching to gun down some bad dudes, as opposed to provide humanitarian aid.
They weren't enough unfortunately, hence the cajun navy. Some sort of civilian auxiliary corps would be awesome.
I'm thinking of more of a social graph where civilians who are going to help in these sorts of situations can be organized more efficiently. For instance, instead of having a bunch of people drive their personal cars out there, going out as a group would improve the individual's abilities to help efficiently.
They also get sent to wage wars of aggression overseas, when the regular army gets stretched too thin.
They will also be deployed domestically to repress public uprisings, etc.
If you want to help people, you're better off becoming a firefighter. Unfortunately, outside of some small community volunteer firefighter groups, this really isn't an option. The National Guard does not fill this gap.
I am thinking more like a level below volunteer firepeople, with some regional and national coordination.