Britain was trying to rationalize its empire. It saw a benefit to centralize and coordinate the colonies. And Britain also had responsibilities to its new dependants - all the North American Indians who now looked to the King to protect their treaty rights. -- snip --
Britain is not a person with one mind. It is a collective of many minds which all want different things, and must act in some kind of compromised agreement. You are not going to get consensus to simply abandon the colonies.
Government policy is never rational in the way an individual might be.
Very much so, not of one mind. A key player was George III, who with Lord North were acting some what similar to apprentice Kaiser Wilhelm (Bill) & steward Otto Von Bismarck a century later. The younger man learns from the older a rather strongarm and unseamly type of statecraft, except that George had a congenital madness about ready to crop up (porphyria) and Bill had a deformed, useless arm -- recent research suggests being cut off from oxygen and mild brain damage as well (I will not call it his shortarm.)
One faction, the ruling Tories (North's group were old Pelhamites) wanted to stick it to the colonialists much as Ireland and Scotland were impoverished in only a generation or two with an initial "only a stamp tax" type foray. Of course they could not say so while inserting the proverbial camel's head under the tent. These upstarts might have blowback to inact change in Britain itself. A few merchants could be co-opted, but already 20% of the British white population the Americans could not.
Give this gravy train up? That would not be real politik.
The colonials, especially wiser heads like Franklin, saw the Scotish/Irish depredations first hand via travels to those lands, and helped to call the bluff. Not wanting to see themselves the losers, the ante was raised in a vicious escalation. In the end, Franklin barely made it out of England without having chains placed on his body, transmorgrified from a eager imperialist place man (lobbist/government opportunist) to a devoted revolutionary. He was supposed to mutter to his nemisis in the Hutchinson papers fiasco, "I'll make your king a little man for this."
Til 1775, the wiser heads, at first especially Franklin, called it one of an aging mother losing her grip on reality. One does not disabuse one's mother, simply puts her under as good care as possible. But this mother had a meat cleaver and like to play mumbly peg with offspring's heads, so we turn the page to declare 1776.
If imperialists let the crown jewel run away, we might have a domino theory collapse. And as the previous poster stated, the (American)Indians were now pledged to be charges just like the colonialists. At least the Indians were easily bought, a long ways away, and would never presume to ask for a place in the house of commons. Time to do a switch like in 1939 White Paper Palestine, and to hell with the consequences.
Your idea is common and common sense, but history is nothing so common or sensical. Emotions tug at our heartsleeves and the head doesnt know what the tail is doing. Just cutting and running goes against nearly any empire, as those characteristics do not tend to make any acquisitions. A worse option, the worst fear of the Tories, was to have the colonies in the parliament, the house of commons. True, there were rotten boroughs and the like, and the southern half of colonies would have been really easy to buy out, but still a 5% to 10% noisy share. Why include in this thead? Because the Tories knew that it would be hard to justify cutting the colonies loose as then they would not only compete on the world shipping market, but could also shop elsewhere. This is really big money and next to no rightist big money person wanted that.
Case in point was Iceland, where 20% of the population _died_ of famine and to some degree of volcanic poisoning in the post 1783 Laki eruption, and it took nearly a year before the King and his exclusive King's monopoly decided to do anything about it, then spent the money on non famine areas, assumedly of politically connected people. Fish was _exported_ out of the island, much as beef was from Ireland during the great 1845-49 famine. (But the 1782-3 famine squelched merchants protesting restriction of Irish exports, possibly because of Whigs coming to power.)
The monopoly of Greenland did not bode well in the 14th/15th centuries extinction, either. It was a European disease back then, government monopolies, and very few ever gave it up willingly while at profit. A soveriegn gave up those trading rights after the poor population was bled dry, generations afterwards, if at all. And the upstart Americans had gotten away with low taxes for far too long, begging to be 'tapped'.