I tend to agree with SKT here.
And BTW, many here who come from the air side of the house see SAR as a CF thing. In fact, the Coast Guard already is responsible for the maritime side of things, with the Air Force providing the air assets for it and the Navy merely providing coordination facilities and secondary assets if, by sheer coincidence, we happen to be in the area. The SAR centres in Halifax and Victoria are jointly manned with the Coast Guard, Navy and Air Force for that very purpose.
I suggest, however, that we have to look at SAR through an historical perspective: The maritime side evolved out of the old lifeboat services. These were very localized volunteer organizations: people from fishing villages located near dangerous maritime transit points would keep and man a boat to save souls at sea if ship floundered on the local danger. Anything on the high seas was, and still is to a large extent, was an "all-hands" matter for any other ship in the area.
Air SAR evolved during WWII, where the explosion in the number of aircrafts, their relative unreliability and the need to save as many trained crew as possible led to each air field having an organization to search for and retrieve airmen whose plane didn't make it. After the war, this led to the Air Force being given responsibility for SAR of downed aircrafts in Canada as a whole.
If one is to look for "savings" in transferring SAR to civilian organization (and I am not dealing here with the quality of the civilian techs vs military ones), we have to keep in mind two things: (1) the fact that the military is already connected into the whole SAR C2 of all departments relevant to the task will be very expansive to reproduce [and, no, I would not let the civilian agency use what we already have, on the naval side at least, these centres are located in restricted access secure headquarters and I would not let anybody in without control over them]; (2) on the air side, the logic behind the development of SAR continue to exist as the responsibility of all commanders - thus, the Air Force would still need to continue to maintain a SAR organization for its own needs, which cannot be delegated to outside agencies [which is why, for instance, even though maritime SAR is a Coast Guard responsibility, Comox maintains its own crash boat for its own planes needs in case of an accident over water].