The US goal of the war wasn't to take Canada
Uhm...Yes it was. Sure, it's claimed that they started a war because they were tired of the British navy pressing 'Americans' into their service, but the only thing they did was apprehend British deserters and this had pretty much stopped as the war was ending. Another reason is trade blockades but those had also been lifted just before the war.
By no stretch of the imagination was the goal of the war to take Canada. That's a myth perpetrated by Canada after the war to over-glorify their victory. Invading Canada was intended as a tool to weaken Britain in order to force them to accept terms pressed upon them by America.
From the internet:
Spoiler
There were several immediate stated causes for the U.S. declaration of war. First, a series of trade restrictions called the Orders in Council (1807) introduced by Britain to impede American trade with France, a country with which Britain was at war; the U.S. contested these restrictions as illegal under international law.[2] Second, the impressment (forced recruitment) of U.S. citizens into the Royal Navy. Third, the alleged British military support for American Indians who were offering armed resistance to the United States.[3] An unstated but powerful motivation for the Americans was the need to uphold national honor in the face of British insults (such as the Chesapeake affair.)
Historians have considered the idea that American expansionism was one cause of the war. The American expansion into the Northwest was being blocked by Indians and that was a major cause. More problematic is the question whether an American war goal was to acquire Canadian lands (especially western Ontario), or whether it was planned to seize the area temporarily as a bargaining chip. The American desire for Canadian land has been a staple in Canadian public opinion since the 1830s, and was much discussed among historians before 1940, but is rarely cited by experts any more.
Let's go through this (putting aside arguments over the lack of credibility in wikipedia articles for a moment).
First, you said "That's a myth perpetrated
by Canada" in regards to the goal of the war being to take Canada.
But then in your quote you use as evidence for your claims (well wikipedia's quote but whatever), "you" say, "There were several immediate
stated causes for the U.S. declaration of war.", the key word here being "stated" (bold added for emphasis). So first you accuse Canada/Canadian historians of acting purely out of bias, then openly accept without questioning the reasoning the US gave when it started the war? Don't you think there might be a bit of bias/misinformation surrounding a war declaration?
Further, let's accept that the US claim that the goal was to capture Canada as a temporary bargaining chip (as your quote asserts). Even if this was the case, this still means that the US for all intents and purposes failed their objective as they failed to make any substantial gains in British North America/Canada.
The only major assertion you are making was that the US did not plan to *keep* the land once they took it, but rather use it as a bargaining chip to affect British policy. However this is irrelevant to the question of who won the war as the US failed to seize the area in the first place and thus was unable to keep it or hold it temporarily to barter with whatever their intent may have been.
"However, historian J. C. A. Stagg states that, "... had the War 1812 been a successful military venture, the Madison administration would have been reluctant to have returned occupied Canadian territory to the enemy".[28] Other authors concur, one stating, "Expansion was not the only American objective, and indeed not the immediate one. But it was an objective",[29] and that "The American yearning to absorb Canada was long-standing...In 1812 it became part of a grand strategy".[30] Another suggests that "Americans harboured 'manifest destiny' ideas of Canadian annexation throughout the nineteenth century".[31] A third states that "[t]he [American] belief that the United States would one day annex Canada had a continuous existence from the early days of the War of Independence to the War of 1812 [and] was a factor of primary importance in bringing on the war".[32] Another says that " acquiring Canada would satisfy America's expansionist desires" .[33] Historian Spencer Tucker tells us that "War Hawks were eager to wage war with the British, not only to end Indian depredations in the Midwest but also to seize Canada and perhaps Spanish Florida.[34]
John Randolph of Roanoke said "Agrarian greed not maritime right urges this war. We have heard but one word - like the whipporwill's one monotonous tone: Canada! Canada! Canada!".[35]"