The British government was deeply in debt after the Seven Years War, so the last thing it needed was to spend a lot of taxpayer money protecting land-hungry colonists from Indians. Hence, the Proclamation of 1763, which prohibited pioneers–even those who paid good money to buy land from Indians–from receiving good title to property west of the Appalachian Mountains.
The Proclamation was a political disaster. It was unenforceable, and it turned the colonists in the frontier areas against the British government. That was one of the decisive factors in the Revolution; since the government didn’t have enough troops to occupy these areas, it had no hope of controlling them without the help of Tories.
If the British had succeeded in crushing the rebellion, would the problem have gone away? Not at all! The demand for Indian land was insatiable. That meant the British government had two unappetizing choices: either spend money it didn’t have to protect the colonists; or leave them to their own devices, which would have led to the creation of militias and, in the long run, military and political entities that were outside the control of the government.
It was the land of no good options. The Revolution resolved the problem for them. Everybody won except the Indians.