In fact, the US maintained a major airforce base (Wheeler) in Libya for 28 years after the 1942 invasion, and still today maintains "forward-operating bases" in Morocco and Tunisia, among other countries world-wide.
In Europe we still have dozens of bases in places like Ramstein, Germany and Rota, Spain.
All are the result of treaties and alliances, some of which put our militaries under single command.
Of course, none of these will ever lead to annexation, but Canada in 1812 is a different subject.
Again, by my count there were nine invasions in less than two years, nearly all defeated.
But had they succeeded, why would permanent military bases, treaties and eventual annexation not have followed?
Finally, let me appeal to an authority on this subject, former President Thomas Jefferson:
So, with British forces expelled, why would Americans ever want to "give Canada back" -- back to whom?
Canada would become just another territory, like the Northwest Territories and Louisiana Purchase.
Oooops. “Wheeler” = Wheelus Air Force Base, near Tripoli, Libya closed in 1970.
And I have too much respect for your posting history to believe that you think we ever invaded the spanish mainland during the Second World War.
With respect to how many times we launched campaigns against the British in Canada during the War of 1812, so what? We invaded the Marianas and Marshals numerous times in 1943-44 because THAT'S WHERE THE ENEMY WAS. Were we supposed to march across the oceans to India, or Australia to fight the British ai 1813?
With respect to Thomas Jefferson's private letters, they expressed to no small degree his bitterness at how impotent he had been to resist British aggression during his administartion. They no more superceded the actual 1812 war aims than, say, do the writings of private citizens of the Confederacy negate the clearly stated aims of the Declarations of Succession of South Carolina, Georgia, Mississippi, etc.