They lacked the option of not doing so.

The war had been going on for eight years, draining the treasury. France, Spain, and the Netherlands had already joined the war. The situation wasn’t improving. The old ministries had been discredited and the opposition in Parliament was ready to call it all off.

The importance of ending the war is indicated by the territory surrendered in the peace treaty. Spain received West and East Florida. The United States was ceded all of British North America west of the Appalachians and south of the Great Lakes.

Aside from disassembling the British North American empire won in the Seven Years war only twenty years previously, the Peace of Paris permanently decided which nation would be the strongest nation in North America in the future. Under the treaty, all of British Canada between the Great Lakes and the Mississippi became part of the United States. This meant that Canada would never be as populous or wealthy as the United States and that the United States, not Canada, would compete with Mexico for control of temperate North America between the Mississippi and the Pacific Ocean.

Only visionaries like Benjamin Franklin and William Pitt understood how important this treaty would be for the future of the world. Within eighty years, the ceded territory south of the Ohio River would be an agricultural powerhouse equal to any European kingdom. The ceded territory north of the Ohio would, by 1865, have an agricultural and industrial productivity as great as any nation in Europe other then Britain itself. The United States, by then, would have won control of western North American by means of hundreds of thousands of immigrant settlers crossing the Mississippi to build new states as far west as California and Oregon.

Addenda: Andrew Jackson O’Shaughnessy covers the realization of failure in Britain very well in The Men Who Lost America: British Leadership, the American Revolution, and the Fate of the Empire.

Throughout much of November 1781, there was still no certain news in London of the outcome of the Battle of Yorktown . . . George III and Lord George Germain, the cabinet minister most responsible for the conduct of the war, had been so confident of victory that the draft of the King’s speech for the state opening of Parliament predicted British success in America . . . On Sunday, November 25, 1781 [Germain and Lord Stormont] took a carriage to see the Lord Chancellor, Lord Thurlow in Great Ormond Street. After a short conference, they collectively decided to summon their nerve and go in person to the Prime Minister, Lord North . . . Between one and two o’clock in the afternoon, the three cabinet ministers arrived at the official residence of the Prime Minister in Downing Street. Although he had long despaired of the war and had many times attempted to resign, Lord North reacted to the news in a state of shock. Germain described how the Prime Minister responded, as if he had been shot, “As he would have taken a ball in his breast.” Pacing up and down his rooms for several minutes, North suddenly opened his arms exclaiming wildly, “O God! It is all over!” North repeated the words many times in a state of consternation and distress.

For the French foreign minister, a French victory over the hated British for the first time in a century was the great achievement of his life.

Germain told the dinner party guests of his just having heard that the Comte de Maurepas, the First Minister of France, was “lying at the point of death.” Wraxall replied that if he were the First Minister of France, it would grieve him to die without knowing the outcome of the great contest between England and America. Germain responded that the French minister had survived long enough to witness the result. Wraxall thought Germain was alluding to an indecisive naval action off the Chesapeake Capes, between the fleets of Britain and France. Wraxall then explained he had meant to say that it was a shame that the dying French minister would never know the final result of the war in Virginia. Germain repeated that the French minister had survived to witness it completely: “The army has surrendered, and you may peruse the particulars of the capitulation in that paper.” Without any visible emotion, Germain removed the paper from his pocket and gave it to Wraxall, who read it aloud while the other guests sat in stunned silence. The news cast a gloom over the rest of the evening as the party pondered the political fallout.

As it was, France did win an important victory in 1783, depriving the British of their North American imperial holdings. Consider how useful India was to Britain in the 19th Century, but with a British population available for wars in Europe. Or Canada during the two world wars but with ten times the population and twenty times the resources.

Not a chip the Bourbons ever got a chance to cash in, of course.

The British failure in each year of the war can be seen in this map: