Actually, the British expeditionary forces in the Americas were
If Great Britain committed serious force in North America during an 1812-like war, they would dominate everywhere besides the Atlantic Coast, where the outcome may be debatable (militarily). I grant you that even with a total military victory they could not politically control the US.
Actually, the British expeditionary forces in the Americas among the largest they deployed and sustained overseas in the period (1783-1812) - during the Revolutionary War, for example, the combined British armies IN the Americas - some 56,000 British troops, plus loyalists - were larger than any other force they had in the field, and numbered almost the same as the British elements of Wellington's army in the Peninsula.
The British contingent in the field during the Peninsular War in topped out around 55,000 in 1813, just before Vitoria; at Waterloo, the British element was about 25,000.
The British forces at Plattsburgh numbered 11,000, including veteran troops transferred from Europe; the numbers for Pakenham's operations in the Gulf were about the same, as well as Whitelocke's force in Buenos Aires...
Historically, the costs of campaigning in the Western hemisphere were simply too much for the British in 1783, 1807, and 1815; they were also too much for the French (in New France
and Haiti
and Mexico), the Portuguese (in Brazil), and the Spanish (just about everywhere else, including their attempt in the 1860s to re-take the Dominican Republic). The French sold Louisiana in 1803 and the Russians Alaska in 1867 because, respectively, neither could hold their respective territories in the event of conflict.
The tribal peoples were, for obvious reasons, very brittle societies; none could compete militarily with a Western opponent, even with external allies, as - for example - Tecumseh's people learned...
A land war in Asia being "one of the classic blunders" is only slightly more justified than a land war in the Americas, certainly by the late Eighteenth Century...
Best,