Yep - the US is bad at fighting insurgencies, but a state military? Over in days. This does not materially change between Canada’s current military vs 5x their current military.

But fighting pissed-off indigenous Canadians? I wouldn’t sign up for that part.

None of this is relevant because the US does not want to own Canada.

Canada's plan was to encourage the US to invade, so the British Navy could attack the US from the Caribbean. The US would get bogged down in the icy Canadian winter, while the Royal Navy took the Eastern seaboard, Mississipi river, and Panama.

The American plan was to throw everything we had at Canada, so it was probably a very good plan.

I don't think it would work anymore.

More practically - in the aftermath of the 1812 War, the US and British North America agreed to demilitarize the border. During WWII, this was preventing mobilization in the Great Lakes region, and Canada proposed undoing the treaty. The US diplomat in charge felt the treaty had historical value and should be kept in tact.

So the US-Canadian border is very demilitarized, by design.