I find something wrong with referring to the Roman empire and COIN in the same sentence - just like it's not useful to judge history with modern ethical standards, I consider it misleading to subject ancient statecraft to modern military perspectives.
The few things that have struck me while reading the occasional book on the classical period is the alien nature of power and perspective. Rome was as much an idea as an empire - in many ways a city-state elevated to regional power through luck of geography. As I understand it they really did believe in a version of Roman might as manifest destiny - and, after the genius of Hannibal had failed to breach their city gates, it is understandable why they had such a view. Believing in inevitable conquest makes for simple strategy, however, and it seems that the Emperor's main obstacle on expansion was domestic distractions. Whenever Imperial Rome's image of invincibility was cast into doubt her response was always strong and resolute. Simply put Rome's honour was the driving force in her ascension to and defence of empire.
Of interest is the way the Principate saw the world - until Christianity kicked off, evidence suggests that the Romans didn't employ maps or cartography. It was rather the idea of a foreign culture that drove the empire's various expeditionary undertakings - contemporary knowledge of the world in writing, including who lived where and what the geography was like. Even when military campaigns were undertaken, the employment of geography appears solely as a tactical consideration rather than what we would see as a strategic or operational consideration. This could be seen in the conquests of Britain, where the idea was to prove the superiority of Romanitas over the British tribes, and all else - including a not too inconsequential channel! - was merely an obstacle to this end. In many ways (and the weakness of this metaphor is that I'm using modern parlance to draw the metaphor) the Roman's practiced an exclusively population-centric strategy. Where barbarians lived and when opportunity was afforded, the legions marched.
Sidetracking briefly: Tactically I've seen some interesting theories that propose the legions as being almost exclusively engineers and the auxiliary forces being the line infantry. The main issue here is that there is good evidence that the legions fought successfully as heavy infantry in the Civil War period, which suggests they were trained and experienced grunts. I do find, though, the idea that Rome exported her occupying legions as engineer forces rather than combat soldiers very interesting.
What I would argue as being beyond doubt is that the Romans were militarily very ordinary, and it was the continuation of successful strategy (the belief in Rome as the civilised power favored by the gods) that was bequeathed to them through a very brutal evolutionary process that made them successful. Tactics can get you so far, but nothing is as strong as a solid strategic foundation. Even the incompetence a hereditary command system or the brilliance of your opposing generals can't undermine solid strategy.
Thus they didn't 'oppress', 'practise FID' or conduct foreign relations as we know it - they rather saw their world as a continuum between Roman and yet-to-be-Roman, and they served that agenda.
As effective as the Roman phenomenon was, I don't see the lessons from her glory days as containing lessons directly applicable to the current state of play.
To quote Colin Gray, strategy is an eternal part of human affairs, and as a contributing (possibly even starting foundation) of strategic knowledge, the lessons of Rome can be applied to America. But that's where the utility ends - direct comparison with Pax Romana doesn't really add much to an understanding of Pax Americana.
In this way Bob's World I agree with everything you have said in about the contemporary world as being of merit. However, your classical linkages (and likewise the entire field of classical-contemporary comparisons) are in my mind flawed as an over-reached argument of minimal benefit. Let historical experience inform us, but don't let it dictate or alter our own reality for historical precedence.
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