Actually, the Revolution to a considerable extent occurred because the French were no longer a threat, having been completely defeated in the French and Indian War. The Americans therefore no longer needed the protection of an imperial connection.
That may have been a factor, but was short-sighted thinking if so. The French were still in Quebec and much of Canada and were still considered a serious threat. The indians weren’t going away — as we know, they continued to be a problem for America for another 100 years.
While the french and the indians had been driven back, the increased territory gained by the Brits meant that there was now a larger and more-cost;y perimeter to defend. The F&I war had been very costly to the British government and it felt that taxes and controls on colonial expansion were needed.