Fun fact about Roman roads: The Romans would build roads as straight as physically possible. Unlike the modern day, where we will wrap a road around the landscape to keep it relatively level, the Romans would direct their roads straight up and down hills to keep them as short as possible.

Also, on the subject of maps of Rome that look like subway maps, the Peutingeriana https://en.wikipedia.org/wiki/Tabula_Peutingeriana is supposedly based on a Roman original and definitely feels like a subway map, prioritizing the connections between cities rather than their correct spatial distribution.