As far as the Mexican War goes, the US could have conquered all of Mexico
No, they couldn't have. Did you guys take over Vietnam?
We would have fought to the last man in our honour and still defended it with success. We would have fought as readily as the Japanese would have in the invasion that would have taken place, had the US not dropped the A-Bomb.
You realize that the US had conquered and occupied the capitol and the Mexican Army was a non-entity by the time of the treaty?
The US in Vietnam, thanks to stupid politicians, never launched an offensive.