In hindsight it might have been better if the British Empire gave the colonists in America seats in Parliament and America never rebelled. It would only be a matter of time before a version of expansion to the West began and America would eventually become the economic powerhouse of the British Empire.
There is the possibility that the British Empire would be a massive "superstate" of sorts that would be practically unbeatable by any other power by 1850. By 1900 it would take an alliance of France, Germany, and Russia to even stand up to the British Empire, butterflies permitting.
The only downside I can see is that it might take the British longer to ban slavery considering the economic interests in the Southeastern American Colonies but it probably would be banned before 1865. Also consider the Southerners are less likely to rebel against a massive British Empire in this scenario.
IT owuld not have stopped the rebellion because that did not want representation in Parliament where they would be completely outvoted. Franklin was even instructed when he went there to never accept any such deal.
Also, it would be difficult with the restrictions on settlement and manufacturing for America to take off in the manner you describe.