You may be interested in an answer I gave some time ago to the question: Was Rome’s acquisition of an overseas empire the result of accidental events or was it a planned expansion into foreign territories?. It's all about the Roman Republic though, not on the imperial period.

This is going to be a really lame answer, but...it depends? The reason for the criticism of Luttwak is that he interpreted the borders themselves as part of a planned, cohesive strategic system that was continuous between regimes, not that he saw everything as ad hoc. So really, the question is how exactly do you mean "centrally coordinated strategy"? There were certainly times and places with high levels of centralization and coordination. The emperor Trajan, one of history's great logisticians, meticulously planned, redefined and reshaped the eastern frontier such that he managed to achieve the conquest of northern Mesopotamia in a single campaign, and the destruction of the Parthian heartland in another one. This required an enormous amount of coordination, troops shifting, and politicing far outside of the theater of war (the necessities of the campaign provided a headache for the governor of Bithynia, in Turkey, several years before it was carried out). So the mechanisms of empire were certainly capable of concerted, highly complex action.

There is also a degree to which the uniformity of the frontier is often understated. Whether you look in north Africa, Germany or Scotland you see a similar configuration of fortlets, border walls and garrisons. Whether or not this constitutes a coordinated policy is a moot point, what matters is that the legions took a similar sort of stance no matter where they were.

But on the other hand, as far as I have read (and I have read a lot of them), not a single one of the preserved letters from Vindolanda, along the frontier with Scotland, can be reasonably interpreted as directives from above. Nor is there really any evidence of the imperial center micromanaging the operations of the forts. What I think can be best said is that the general fronter system tended to be replicated across space, but that within that the decision making was primarily loca. Except, of course, when the emperor wanted to go out a-conquering.

I studied this question a while back. If there's any recent scholarship on the matter I won't be aware of it, but from my reading a good decade ago:

Luttwak has had more than his fair share of critics, as you say. Historians like Isaac^1 would argue that we do not have "evidence that suggests central coordination." He'd say that to assume a grand strategy, we'd need to assume:

• That the Romans made rational, considered decisions on when and where to wage wars.
• That the Romans consciously chose where to put their realm's borders.
• That the Romans based these choices on geographical considerations.
• That, therefore, the Romans must have had planners with good knowledge of the realm's topography.
• That Roman war-goals had to be about promoting peace and security for their provinces.
• That it is possible to deduce the strategical and tactical functions of forts and troop-emplacements from physical archeological remains.

He'd say there is no actual good evidence for any of these assumptions, and indeed plenty that contradicts some of them.

it almost seems like emperors and the political elite had a well-defined set of "national" interests and were capable of allocating resources on an empire-wide scale to achieve these interests.

That's the question, isn't it? Isaac would say no. Or rather, that this "national interest" would be quite different from what we'd assume today.

Would the Romans even have recognised the need to defend their provinces from hostile incursions? Isaac claims the Romans didn't really see the defence of civilians as a primary task of their army. Rather, it was about ensuring the prestige and control of the emperors, the safeguarding of tax-collecting, and control over peoples and tribes rather than over geographical borders, which would have been a nebulous concept at best in an age of limited maps.

So Isaac paints a picture where the deployment of troops in the East (his area of speciality) were deployed for offensive campaigns against the Parthians, and not for defence against them. The Parthians were never seen as a serious rival let alone an existential threat to the empire until Byzantine times anyway. Nor were the Germans ever in a position to be more than a nuisance to the Romans in the first few centuries of their empire. No need for defence, then.

Indeed, Isaac argues that the most important role of the legions was maintaining Roman control and dominance over the subjugated provincials. Policing rather than defending.

He admits that some effort was made to defend against nomadic raiders with forts and watchposts, but no defences were ever in place against larger incursions. Isaac denies that the limes was any sort of military frontier (page 408-410) and that the placement of forts was anything but ad-hoc happenstance. He claims most would grow, for example, around some randomly placed marching-camp that was enlarged and strengthened over time. The idea of "defence is depth" is anachronistic and the split in the army that occurred from the reigns of Diocletian or Constantine onwards should be seen as a split between a field army and a territorial army, rather than a mobile army and a border-guard.

Of course, this is just one view, and one that has a number of problems of its own. Wheeler^2 criticises historians like Isaac (and, in this article, Whittaker) harshly and says they're too heavily influenced by their own doctrinal background as historians of the Annales-school, though I can't comment on the accuracy of that. He points out numerous errors and attacks many of Isaac's assumptions, though:

• Isaac's speciality is the east. There was never a line of fortifications in the east like there was in the west, because any large Parthian invasion could only come along a few well known invasion-routes, along the Tigris or the Euphrates rivers usually. (And incidentally, this may be one factor in the Byzantines inability to effectively defend against the Arabs attacking from an entirely different direction, centuries later.) He doesn't really explain the types of borders seen along the Rhine or in North Africa.
• Unlike what Isaac claims, the Romans did have terms for defensive borders, such as probolos. - "defensive bulwark." and applied them to the conquest or annexation of new territory.
• The Romans also had a concept of geographical features as borders, which can be seen in Republican-era treaties such as the one that fixed the limits between Roman and Carthaginian zones of influence in Spain prior to the second Punic War. Again this is in contradiction to some of Isaac's stronger claims.
• A lot of his points about the legions' main function being internal security is based on his studies of Judea, which he and everybody else admits are exceptions to the rule.
• It's hard to deny that as time goes on, almost all troops are positioned along the borders of the empire, rather than in the interior. That doesn't really match the "policing duties" view.
• Isaac also fails to explain why, in the 2nd century A.D., the legions are spread out thinner and thinner along the frontiers. (What Luttwak describes as the "Flavian system.")
• Finally, it's dangerous to argue from hindsight. Isaac may say the Parthians and the Germans were no threat to the Roman Empire in the early principate, but just because we know Rome was too strong to be easily destroyed by such doesn't mean the Romans didn't feel threatened. There's enough indication that the Romans did believe their neighbours posed a serious threat to the continued existence of their empire, as indeed proved to be the case in later centuries. And feeling threatened is plenty of justification for defensive postures.

Someone like Brunt^3 would argue that we do see emperors allocating resources based on what they perceive as national interest, but not in as organised or doctrinal a fashion as Luttwak would assume.

Brunt would say that in the early years of the principate, as in the later years of the republic, the Roman attitude and philosophy was one of offensive warfare, not defence. The idea of imperium sine fine is a big one in Roman propaganda, but Brunt would argue that the Romans may actually have believed that they could or would conquer the world. Alexander had, after all, and Caesar had had serious plans for a similar campaign when he was assassinated. Even as late as the 3rd century Roman propaganda claims they rule the world, except for the parts not worth conquering. It's possible that the Romans always planned to one day get around to conquering those last bits. You could call that a grand strategy if you really wanted to, though not perhaps a realistic one.

In practice there is a gradual shift towards defensive behaviour, but in Brunt's view this is not the result of any rational policy, but rather a combination of chance and circumstance: the Julio-Claudian emperors, for the most part, are inexperienced soldiers at best, and to allow subordinate generals to wage wars of expansion risks usurpation and civil war. So conquest is put on hold, but there is never a conscious choice to stop expanding. (See: Claudius.)

Until, that is, Hadrian. It's hard to argue that Hadrian wasn't following a conscious, defensive policy in his re-organising of the empire's provinces, the abandonment of Trajan's conquests, the construction of linear borders in Britain and North Africa, etc.

But does that mean that from Hadrian's reign onwards there is a new Roman doctrine, a new grand strategy? Probably not. Rather, subsequent emperors mostly continue Hadrian's policies because they work, making their own chances as the need arises, but are perfectly happy to wage more offensive wars when they sense a chance for glory or need military credentials to prove themselves.

Brunt also notes that if Hadrian had followed a truly rational defensive policy, he'd have abandoned Britain rather than (or as well as) Mesopotamia, but that would have been too big a blow to Roman prestige and an impossible sell back in the capital.

It's also hard to deny that the defensive posture of the Roman army in the late Principate, spread along the borders as they were, may have been good at stopping raiders, but proved utterly inadequate to the challenges of the 3rd century. So if these troop-dispositions were based on some centrally planned strategy, it wasn't a very farsighted one. The changes in the Roman army and its deployment that occurred in the 4th century may have been meant to alleviate these problems, but probably had at least as much or more to do with attempts to increase internal stability and reduce the number of civil wars by giving the emperors control over the new field armies.

In conclusion: Some individual emperors do appear to have had a clear vision of how to allocate their empire's resources to achieve what they saw as the optimal goals for Rome. This could be offensive, as Trajan showed, or defensive minded, as Hadrian demonstrates. But there is no good evidence for cross-generational doctrine the likes of which Luttwak assumes, and much to indicate that the overall Roman dispositions of troops and fortifications were the result of a gradual accumulation over generations of individual decisions and ad-hoc happenstance. Some of Luttwak's critics go too far in denying any kind of Roman rational planning or defensive thinking whatsoever, and despite all its shortcomings his book remains a fascinating read, but there just doesn't seem to be enough evidence to make a case for a real Roman "Grand Strategy."