The Proclamation of 1763, which forbade colonial settlement west of a line that ran along the Appalachian Mountains, was indeed designed to save money for the Crown. Let us look at reasons why this was the case.
The French and Indian War fought in the colonies had driven the French out of Canada and all lands east of the Mississippi River. For the American colonists, this meant that they could move into the Ohio River Valley, a very fertile region that had been fiercely contested by the British, the French, and various Native American peoples for decades. This was, in fact, where the French and Indian War had begun.
But many of the Native peoples in the region were deeply concerned about new colonial settlement, and they fiercely resisted incursions. The most famous example of this was the so-called "Pontiac's Rebellion," a broad-based Native resistance movement that required British military intervention to quell. The Crown recognized that if white settlers continued to enter these lands, that they would require a large, sustained, military presence in the region, which would be very expensive. So the Proclamation was, in part, intended to save money on this count.
Colonists, especially wealthy land speculators, bitterly objected to its terms, and the Proclamation never really stopped settlement in any case. Over time, it was gradually revised by treaties with Native peoples, but historians generally agree that it was the first phase of the imperial crisis that emerged in the colonies in the 1760s.