Disclaimer: So I am going to steal part of my own answer from a post I made here on reddit, about whether or not the Revolution was justified ( How justified was the American revolution? Were the colonists justified?
Answer This is sort of a difficult question to answer since it is an opinion question and we, generally don't play the "what if" game here. That said, I think the easiest way to address this question is, what ultimately caused the Revolution, and seeing if Great Britain attempted to truly avoid revolution.
If we look at it, from the perspective of the colonists, they had many reasons to want to revolt against Great Britain. In my opinion (and the opinion of many historians, such as Gary Nash), the American Revolution was much more heavily supported and seen as a necessity for poorer people rather than the gentry. However, I believe there were plenty of reasons that could justify war with Great Britain during the 1770s, especially if you were not part of the gentry or wealthy merchant class. Among my reasons for saying this is that following the French and Indian War, Americans were suffering from a harsh economic depression. Part of this was that due to the fact that starting in 1764, the British started banning paper money. (George Athan. The History of the British Empire, from the Year 1765, to the End of 1783. pp 6.) The act itself is known as the Currency Act of 1764, which devastated the colonies. This is significant because during the War, states started issuing paper money when gold and silver ran out. By some estimates, half or more than half of all currency in circulation by the 1760s was paper money. When the British Empire rendered it worthless, and forbade colonists from paying debts or buying goods from British merchants, you had entire life savings become worthless almost instantly. Many people lost their homes, businesses, and farms due to this.
The British also began to strongly enforce mercantilism, where they forbade the colonists from importing goods from anyone else besides Great Britain. This was extremely costly too because they British forbade colonists from creating their own goods -- even things like textiles for clothes or iron for building houses couldn't be processed and created in America. Raw iron could be turned into something called "Pig Iron" but then the raw goods would be shipped back to England. Then after it's refined, the iron would be shipped and sold back to the Americans at a very steep price. For a series of colonies that were already struggling financially, it was very painful for the average American family.
Great Britain also did very little initially to try and hold off revolution. For the most part, many within Great Britain doubted that the colonists would unite together, and even more unlikely, would coordinate efforts to fight off the power of the British Crown. By the time they realized how serious the colonists were about their demands, war had already begun.
In reality, the Revolution actually changed the way people interacted with their government in so many different ways. Historians refer to this as "high politics" and "low politics." The high politics are the politics of the elite -- people like George Washington, John Adams, and Ben Franklin and how they were able to vote, pass laws and have conventions. This is of course was the absolute backbone of the Revolution. But most Americans couldn't go to the conventions. Most Americans weren't represented during the era -- at least not early on. But the Revolution was just as much a part of the lives of lower-class Americans as it was to the gentry. Why? Because they chose to get active.
From the mid-1760s until the 1790s, entire generations of lower-class, working-class Americans took to the streets when they saw injustices happening all around them. It would sometimes take the form of attacking tax collectors or storming British ships and dumping tea over board. But other times it would manifest itself as "armed regulations" where Colonists and early Americans alike took up arms against their governments. Some members of our society which were mostly neglected, including women (who weren't even legal citizens) also played roles in these unofficial forms of politics. In some moments, African-Americans and even those who were enslaved stepped outside the bounds of their own roles and fought for the freedoms that so many Americans craved. Ultimately, through the window of the Revolution, they saw the ability to advance themselves.
So I throw the question back to you. Given the fact that Great Britain kept tightening its fist while Americans saw greater promise through their own Independence, did they have more to gain by fighting for their own freedom?