Perhaps I expressed myself incorrectly.
The operative word in my sentence is "policemen", not "operating on our coasts", which we already do.
Our work does begin at tidewaters, even before tide waters: My name is on a list of recipients of a CDS unit citation for the Oka crisis. We provided patrol boat support for the op and closed the river to inter-reserve traffic.
We do sling sandbags too: In the Winnipeg flood, we repatriated all the navy heavy RHIBs by truck or air to Winnipeg and provided the "heavy trucks" of sandbagging to remote areas accessible by water only.
We do our share of Sovpats: We are always sailing in our area of responsibility (Canadian waters). Anything on the water in our area of responsibility, we try to identify and track in our common picture system.
And we do all this in defence of Canadian sovereignty. But policing, that is enforcing the laws of Canada within the Canadian borders or EEZ is not our job anymore than the Army patrols downtown Montreal for parking infractions or the Airforce will inspect the maintenance logs of Air canada planes to see if they are up to date.
The Arctic, whenever it is ice free so that commercial exploitation can occur is just as ice free for our current type of warships. That is why, for instance we do operate frigates, MCDV's and submarines in the high Arctic in the summer months in support of the defence of the Arctic. However, being able to operate in the ice would serve no purpose and it is only wanted as a form of police presence by the government. The Coastguard can carry out this "presence" role better and make more economical other use of the hulls at the same time, for ocean research/rescue/ice breaking services to commercial traffic, etc.
Lets face it the only military role an icebreaker could have is to go and "attack" a "military" target in the Arctic. That would be akin to sending a four inch long snapping turtle across a whole school gym to go after the other side's snapping turtle (for those of you unfamiliar with icebreakers, they usually don't move through ice much faster than a fast walker would walk on it.). When you otherwise have at your disposal a seagull that can break a turtle's back with its beak, such a slow motion chase becomes ridiculous. If there is a military threat to the Arctic within the iced area, air power will be required, not slow Navy icebreakers. (Historical aside: Funny enough, the last time the RCN operated an icebreaker as an Arctic Patrol Vessel [HMCS LABRADOR], she was mostly used in support of the RCAF in helping it set up the DEW line of radar stations.). If the military threat is not itself a slow icebreaker, then it is because the conditions are propitious to employment of standard warships by both side.
P.S GR66: The planned number of CSC's is 15, plus the 6 to 8 AOPS, which are the abomination I would like to see replaced by proper OPV's, whether along the line you propose or the one I do. I picked the one I presented because, unlike the larger OPV's or AOPS, they could be mostly manned and operated by the reserves. A fleet of 15 CSC, 2 AOR, 12-14 OPV such as the one I propose and 4-6 submarines would serve us great. If two Mistral type amphibious ships could be added, it would be even better.