"So the real question to ask is: what ideas and vision gave Rome that coordinated energy in the first place,"

Taxes.

I would conjecture pre-Roman when groups would sack a town they would kill all males and enslave the rest. Taxes changed the game. This created a concept of managing states. Instead of killing everyone in a village - you wanted them to work hard and pay taxes. This also had an unforeseen side affect: if you were a good tax payer you were protected. People wanted to be a Roman citizen. The Romans would destroy anyone taking their tax money. You could safely produce a crop or raise cattle. Other cultures pre-Roman had taxes but were always caught up in ethnic cleansing - thus destroying their tax base. Romans could care less: Spaniard, Syrian, Egyptian, didn't matter: just pay taxes.

If you inflate currencies to the point taxes mean nothing: doom.