From this side of the Atlantic, it was a different problem. Though the American Colonies brought great profits to their shareholders - mostly Colonists themselves, but also the Royal Family - they were a drain on the Exchequer. Parliament was expected to provide for their defence, both by sea and land and for public order. This meant troops and ships and a lot of money. Direct taxation was not possible as the Colonies were Charter Companies rather than Parliamentary Boroughs and the King in those days paid no tax. Choices were limited.
1. Indirect taxation, tried but unpopular, a threat to public order which would have necessitated more troops, which would have cost more, and so on.
2. Abolition of the Charter Companies and the establishment of Boroughs within the Colonies, each required to return a Member to Parliament. Given the time and risk involved in getting across the ocean to Westminster, this would have been impractical, and anyway the King wouldn't allow it.
3. Do the above but set up an American Parliament . That would have given the Colonies more autonomy and allowed them to raise taxes to provide for their own defence. But the King wouldn't allow it as it would have cut his profits.
4. Cut them loose. The moderately-profitable trade between British and American merchants would continue (business peoople are nothing if not pragmatic), but the Colonies could take care of themselves.
Eventually, route 4 was followed, with a face-saving pretence at putting the Revolution down. Bear in mind that Britain was one of the most powerful nations in the world at the time, so losing to a rag, tag and bobtail Colonial militia, even with the support of some of the First Nations and some crack French regiments, could and does indicate a general lack of commitment on the British side. In the end, it was no loss to Britain, as India and the Far East were far more profitable than America had ever been.