Agreed. Though I suspect most of your parallels apply to all nations with a long history of successful warfare.
Germany and France both had brief and storied runs as dominant military powers, but both lost badly in the end. Although Napoleonic France and Nazi Germany could win battles, they were unable to fashion war-winning strategies.
In another parallel with Rome, the US is a status quo power in its strategies but a revolutionary power in its appeal. The US aims to preserve the current favorable international order that emerged after WW II, yet it also promotes modernity, capitalism, human rights, and democracy. For much of the world, these are appealing but deeply disruptive.
With that in mind, it is a sign of both a lack of realism and a lack of intellectual grasp of grand strategy that the US has not fully embraced and promoted a reform agenda in the Muslim world. In the battle of ideas, human rights, democracy, and fair treatment of women would do much to counter Islamist radicalism and subvert the medieval mindset of Muslim societies. The terror war is early in its middle stages though and such an approach may yet be adopted.