Sovereignty in the High Arctic

Apparently our government is planning to spend $7.4 billion on half-a-dozen ice breakers to patrol our northern waters and particularly the NorthWest Passage which, in a warming world, is starting to become a more viable trade route.
I'm not dismissing out of hand the whole idea of protecting our sovereignty of the area (it is probably safer from abuse in Canadian hands than in the hands of many other countries I could mention), but several things occurred to me during the reading of the article (in no particular order):

• How can anything cost $7.4 BILLION? I know they are big, rough, tough ships, but they are just ships. Surely billions are for country GDPs, Pentagon budgets and the like.
• Oh, and by the way, do we actually have $7.4 billion?
• It seems pretty ridiculous to me to apply the UN rule of sovereignty extending 12 nautical miles (22km) from a nation's coast to what is clearly the interior of a country, thousands of miles from any other country. The legality of territorial waters is a hugely complicated field with considerations of contiguous zones, continental shelves, economic zones, special cases, etc, etc, but is it really relevant here?
• The 'use it or lose it' principle seems somehow quaintly anachronistic in a modern litigious world. Does Mali use the miles of desert in the interior of its country or Denmark use the interior of Greenland? It seems duplicitous then to insist that we use some of the more-out-of-the way bits of Canada in order to lay claim to them.
• Having a few ships patrolling the High Arctic waters does not seem to me to offer much assurance anyway. What do they propose to do if an American nuclear sub or a Russian fishing boat decides to pass through the area regardless? Shoot at it? Give it a good telling off?
• From what I can gather, the main thing driving all this is actually the ownership of rights to possible oil and mineral exploitation, rather than trade and tourism routes.
• That nice Mr. Putin has apparently declared the North Pole Russian territory due to a new reading of the continental shelf rules. Do these people sit up in bed thinking up new ways of antagonising the rest of the world and creating new arguments where none existed before?
• Wouldn't it be much more sensible (and much cheaper) to just negotiate a binding international treaty, or am I just being naive?