The end of the War of 1812 seems like a good setup for a total British victory, wiping America off the map entirely. Washington is in ashes, they've won victory after victory, and their only real distraction - Napoleon - seems over and done with that treaty being written at the same time as the one for 1812.
Fittingly, the British started negotiations with embarrassing concessions for the Americans. We from the future know Jackson won an insanely one-sided victory in New Orleans and the treaty essentially set things back to how they were before the war.
But the negotiators at the time had no idea of knowing that, as Jackson's victory came after the settlement was made. So, why did the British change? Why not use this opportunity to take back some of the Empire and silence the whole "republic" issue while there's nothing in their way?
The British never intended to subdue the United States - that was never an official goal. After the Battle of Plattsburgh was lost in the north, it was very unlikely that the British could secure any leverage concerning territorial gains during the Treaty of Ghent negotiations. After a long and wear war with Napoleonic France, the British simply wanted to achieve the objective of repulsing the enemy from her colonial territories - with the remote chance of securing an Indian buffer state in what is now the Ohio Valley (a British goal also during the Treaty of Paris negotiations after the War of Independence).
After the War of Independence there was never any real intention on behalf of Britain to conquer the United States.