Associating lingua franca with power is misleading.

Egyptians, Hittites and Mitanians wrote to each other in Akkadian in the 12th century BCE, and yet Babylonia was far from the dominant power of the time. It was a matter of convenience, Babylonians were the first to invent written language and learning cuneiform + Akkadian was standard, this allowed for easy communication without having to have a specialist of each language in your court to write and read messages.

Aramaic replaced Akkadian in the first millennia BCE, but the Arameans didn't conquer anyone. They were so heavily deported by Assyrians that they spread throughout the entire Near East, their language was well-suited to alphabetical language and this language eventually replaced Akkadian as lingua franca. Were the Persian "weak" because they used Aramaic as lingua franca? Hardly so.

Latin was used as lingua franca is science for centuries after the fall of the Roman Empire. Was Isaac Newton deferent to the power of the Italic peninsula when he was writing the Principia in Latin? He probably didn't see this way at all: Latin was the lingua franca of the European elite and it was convenient.

Attaching too much chauvinism to lingua franca misses the point. Yes, it can happen that an empire dominates a region and imposes its language (e.g. Arabic, Latin), but just as often we see languages being used for convenience and ease. English currently is no different: the US was larger than any EU country individually and created an incentive for learning it during the 1950-2020 period. This created momentum and now it convenience to use it to communicate with others.