Without Halifax, Is Canada/British North America "Worth It"?

Basically what it says on the tin. If, by some turn of events, the US managed to secure Halifax, either by conquest in the Revolution or the War of 1812, or by having Nova Scotia (for whatever reason) throw in with the 13 Colonies, is Canada/British North America "worth" keeping? Can the territory be maintain without the easy access Halifax provided, and would the British simply "give up" on the territory all together?
 
A lot of historians consider Canada an albatross hanging around Great Britain's neck throughout the 19th century. There definitely could be room for a lot more aggression if there's no Canada to defend.
 
St John's still provides decent access. Really Halifax was made less useful by the loss of the 13 Colonies (it's a great stop off from Britain to the US, not so good for accessing Canada).
 
I'd imagine yes - since you still have St. John's and Newfoundland being general access points to Canada, and Canada itself full of people loyal to the Crown worth defending.
 
Also, I would suggest that an arrangement whereby Britain loses Nova Scotia, a peninsular territory that's practically an island, but keeps the rest of British North America is low-probability. Why does Britain lose only the least vulnerable portion of its North America empire?
 
Newfoundland & Labrador were not integrated into Canada until after WW2. How to British treat the mainland in relation to not having Halifax as an example does raise interesting repercussions. Would the British lose interest in mainland Canada and focus their efforts on Newfoundland to protect their fishing interests such as France who has maintained Saint Pierre and Miquelon.
 
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