> I consider setting up empire-wide infrastructure to be something that largely happens due to socioeconomic forces and the environmental conditions of the empire, not something that 1 guy decides to do alone
Yes, well, that's not how history actually happened. I suggest reading more about Augustus the individual and the decisions he made. A different person would have made different decisions – which yes, would have reverberated down to the common man in "Ohio", especially if his formerly peaceful locale is now a warzone or if his children are drafted into the military.
Augustus laid the bureaucratic and financial foundation for the Empire and without him, there's no guarantee that the Roman Empire actually exists. So again, no, the empire would not "have been led by someone slightly different and perhaps had slightly different borders." It may have splintered into eastern and western divisions sooner, been overrun by barbarians more quickly, or fractured into the pieces held by the various factions.
https://www.worldhistory.org/article/905/reforms-of-augustus...
This exact same scenario has happened many times WRT Muhammad, Napoleon, Constantine, George Washington, et cetera et cetera. The idea that individuals are just interchangeable cogs is just a 20th century cultural trope, not an accurate reading of history.