“All the Roman Empire needed was a banking system, a postal system, and universal compulsory education, . . . “
A property recordation system and a court system that impartially enforced contracts would be a must also. Universal education, probably not so much. The US was the already the most powerful country in the world by the beginning of the 20th century—before universal compulsory education in the US.
It’s true that federal laws about it didn’t come about until 1918, but parts of what is now the US has had universal compulsory education in some form since the 17th c at least, in the form of parochial schools attached to religious sects. Massachusetts systematized it a statewide basis in 1852, but most people had some kind of 3-r’s before that, even if it was taught at home. Rural one-room schools were around here in Michigan as soon as European-descent pioneers settled, and the first high school (still stands, no longer a school) in my hometown is from sometime in the 19th century. The brick multistorey high school (now gone) dated from the early 20th.