Huey, there are very few (notice I said few; I'm not looking to restart a discussion on active shooter scenarios) civilian law enforcement events for which the military would be a better match than civilian LE, IMO. As for non-law enforcement (CBRNE events, disaster response, etc), the federal, state, local and tribal governments have multiple layers of response redundancy, and in cases where the military is well-suited to support local officials, there are plenty of resources available. However, note that I again said the DoD is in a supporting role. The only circumstance in which the DoD is a lead federal agency in an emergency function is when it deals with public works, and the Army Corps of Engineers fills that role.
Mug, feel free (minus the tinfoil, of course
).
Anyone wanting to probe my new found knowledge (and limited experience), I'd be happy to tell you what I know.