Between Pyrrhus and Rome "marching in" lies a period where Spartan hegemony was eclipsed by Thebes and Philippos II defeated the Greek/Theban phalanx by superior tactics, notably the shock cavalry that became Alexander's trademark. No steamrolling involved.
Your timeline is kind of messed up. Pyrrhos came long after Philippos and Alexandros; his war, in the 270s BC(E), was a product of the Roman expansion into Megale Hellas. His army, which included phalangitai on loan from the Makedonian king, a mixture of light cavalry (which was excellent in southern Italy; the 'Tarantine' system of skirmisher cavalry was one of the better available in the Mediterranean) and heavy forces like the hetairoi, and elephants from the Arche Seleukeia, was definitely a model of the Hellenistic military system. (Although there were obviously improvements in the system later; the military never just 'stands still', there is always innovation to an extent. In this case perhaps the most salient point is the establishment of a corps of
hysteroi pezhetairoi in Makedonia, which were able to fight on uneven ground better than the normal phalangitai.)
So the problem wasn't really a differing - or at least inferior - military system at all. Tactically, the Hellenistic system utilized a wider variety of forces than the Roman, and if properly used had the advantages of the Romans along with those of other units. The establishment of units like the
thorakitai and
thureophoroi (which were derided by Romans as being 'imitation legionaries', but which actually predate Roman contact in the Hellenistic world by some decades) allowed Hellenistic armies to fight in flexible formations that didn't have the disadvantage of the Makedonian syntagma when fighting on broken ground. Problem was, the later Hellenistic monarchs failed to maintain this combined arms approach, instead concentrating on the parts of the Alexandrine system that looked more prestigious, like units of elephants or massive multi-decked ships, and allowing the combined arms-based military to erode.
I think that the event that is most instructive here is the Battle of Magnesia, fought between the Seleukid monarch Antiochos III Megas (one of the more enigmatic and yet successful rulers in history...at least up to that point) and the Romans with their Pergamene allies; the battle in general played out much like that of Ipsos, whereat Antigonos Monophthalamos' superiority in cavalry was wasted by his son Demetrios Poliorketes, who upon defeating the cavalry forces of Antiochos I, fighting for the allied forces, decided to pursue the enemy cavalry off the field, allowing the allies to gain a local superiority in the center with their light infantry, and then bombard the Antigonid infantry until Antigonos himself was killed and his army disintegrated. So it was at Magnesia, sort of: Antiochos III, in charge of his own cavalry, drove off elements of the allied horse but then pursued off the field, allowing the Pergamenes to dart into the gap his cavalry had left and surround his infantry. Had the Seleukid king not made that critical error, the Romans were at a significant disadvantage, and I don't rate the chances of their victory very highly...(Of course, it was a mistake for him to even engage in the battle at all; he should've waited for the Romans' own political issues to force them to withdraw, whereupon he could have dealt with the Pergamenes at his leisure.)
JEELEN said:
So, Greece's powerbase was already eroded by internal warfare and Macedon before the Romans took it in steps, as noted below.
Not much more significantly than it was when fighting the Persians, I think. Athenian attempts to export the revolution following the institution of Cleisthenean democracy had done a good deal in increasing divisiveness amongst the Hellenic states. And it wasn't, as previously mentioned, as though the Greeks stood as one united front against Persia. Argos was the most heinous offender in failing to join the allies at Plataia and Salamis, of course, and the northern Greek states like Thessalia, Makedon, and the Boiotian cities were on the whole collaborators with Xerxes' forces. I think that the comparison is more instructive when one looks at the opposing methods of Persians and Romans. Darius and Xerxes made their attempts at the end of a logistical tether, in only two major efforts (490 and 481-79, natch). When the Persians ceased their attempts at blatant conquest, and instead sat relatively idly and played the Greeks off against each other (as in the Peloponnesian and Korinthian wars), they had much greater success: the Peace of Antalkidas, which ended the Korinthian war, was called the King's Peace because it essentially showed that the Great King in Susa was able to dictate to the Hellenic states the terms of their political arrangements, and those terms involved Sparte becoming unofficial hegemon. (It was mostly due to Persian internal problems and the overall erosion of their empire due to rebellions and weak leadership that Persia failed to capitalize on this; one must remember, after all, that Megas Alexandros was a friggin' Great Captain of History, and without him at the helm the Makedonian invasion would certainly not have seen the success that it did. Even a Iason of Pherai or Mausollos of Halikarnassos would have been hard pressed to secure the same magnitude of victory.) This Persian policy can be easily likened to the later Roman one, seeing as the Romans supported the Greek states against the Makedonians, and then upon the elimination of that enemy had achieved hegemony by default.
Playing off on intra-Hellenic dissension and conflict instead of overt attempts at conquest, it cannot be stated often enough, was the prime factor in Roman success.