George, the RCMP are definitely more para-military than other services in Canada. I watched a graduation parade at OPC and I was standing next to and chatting with a paramedic who was former CF. When the graduates marched in we had to avoid looking at each other to keep from laughing. I haven't seen bear-marching like that since the Army Cadets on remembrance day, not to mention there dressing and cadence. In comparison the RCMP have always looked very very smart everytime I have seen them march.
But in all seriousness an instructor once explained to me that the RCMP was both the national police and the federal police of Canada. What he meant by that is the RCMP maintains databases such as CPIC and VICLAS for use by all police in Canada. Conduct investigation into matters that cross jurisdiction (especially provincial borders) and are of national/international interest. As well as being the senior member(wise old man on the mountain) of the police community, being the repository of knowledge and conducting advanced training for all police services at the Canadian Police College. All these functions are what my instructor called the "national" role of the mounties and are a kin to that of the FBI. In spite of a bit of an erosion to my lasts point about CPC the RCMP before these functions very well for Canadians. But as Blackhorse 7 stated above it would be nice to see more focus on this role.
The "federal" role as my instructor put it is more a kin to that of the Gendarmerie Nationale of France, the German Bundespolizei, Italy's Carabinieri or the Gardia Civil in Spain. This is a role that protects and guards federal properties, the nation's vital infrastructure, borders, sovereignty and transportation network. As well as being a reserve of bodies to be called upon whenever extra police are required in any part of the country. This is a role the RCMP don't exactly fill and are taking on less and less because of a focus turning to local and provincial policing.
The Ports Police are gone and the Mounties don't police the major airports anymore and the CN and CP Rail Police most people have never heard of. CBSA and Customs seem to be stepping up a bit but CATSA is a mess and people are screaming for an armed Coast Guard. Federal law enforcement needs a lot of thought and I think it is worth looking into what is going on with our friends and I am sure they won't mind, because after all we are friendly Canadians, eh buddy
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Canadian police in my opinion rely too heavily on an American model of policing which has strength and weaknesses but might not suit Canada as well as some would like. It is worth looking at a European model to at least see if there is anything there to benefit Canadians. At the very least it is something to put the American model up against and pick and choose what would work best for us here in Canada.