Timing and finances would be my answer. In short, once the legion diverges from the phalanx, most of the phalanx's users would've had little reason to notice or adopt the changes until war broke out. By the time it does, Rome is massively wealthy and more or less unstoppable by the quantity and quality of the forces it can throw at its enemies. By this point, being able to organize a legion means more than just tactics or equipment, but also experience, numbers, logistical organization, and money, money, and more money, and there was no single power that could match Rome in those categories.

You're right that phalanxes predominated in the post-Hellenic vacuum left by Alexander's demise; at this time, Rome was still one player among many, not even in control of all of Italy yet, and it was also roughly around this time that it was embroiled in a war against the Samnites. I note this because at the time, Rome also used the phalanx, and was struggling because it lacked flexibility for anything but head-on clashes, and the Samnites were mountain fighters who refused to meet the Romans head-on. By most recountings, Rome adapts by developing the manipular system, the "phalanx with joints", with the hastati/principes/triarii lines that you might be familiar with. This is probably the first organization that's distinctively Roman, and it is with this system that Rome would go on to contest Magna Graecia against Pyrrhus, Sicily against Carthage (the First Punic War), and eventually, dominance of the western Mediterranean against Carthage (the Second Punic War).

While all this is going on, though, Alexander's successor states are still beset by fighting against each other, and they maintained their phalanxes for a pretty good reason: they were largely facing other phalanxes. The additional tactical flexibility afforded by Rome's legions seemed to matter little if infantry battle was settled by frontal assault, and the phalanx's hedge of 16-foot sarissa was unbeatable in frontal combat. There was still plenty of tactical development, and the subject is heavily contested by historians, but the short answer seems to be that phalanxes and legions largely existed in separate spheres for much of this time, with the notable exception of Pyrrhus' exploits in Magna Graecia. This held true until the Second Macedonian War, which brought the veteran Roman legions against the Hellenistic-model armies.

By now, Rome has several major advantages: having just beaten Carthage in the Second Punic War and seized its riches, Rome is quite wealthy and possessed of veteran infantry who have been fighting, in some cases, for twenty years. It has the organizational experience to project those infantrymen and their logistical baggage all over the Mediterranean and a deep manpower pool of its own citizens and its Italian socii allies. Rome's wars against the Hellenistic successor states overwhelmingly go in Rome's way, and with each victory, more and more Greek city-states turn to Rome (and thereby add their manpower to Rome's auxilia pool), and more Rome's war chest swells. This is a piecemeal process that lasts more than a century, and there are reports that there are rulers like Mithridates VI who attempt to copy the Roman legion. By this time, however, no amount of tactical tinkering can change the strategic situation: Rome was powerful enough to hold off Mithridates while dealing with a massively destructive revolt by its Italian allies (the Social War, which ends with the granting of Roman citizenship to the socii), while dealing with one of its most turbulent political periods prior to the complete breakdown of the Triumvirate period. This would be the ultimate reason why nobody was able to copy the legion: by the time its (somewhat marginal) tactical superiority becomes marked enough to be noticed, its real strength lay not in its tactics or equipment but in the Roman state apparatus that sustained and equipped it, and in the veteran footsoldiers who fought in it, and those could not be easily copied.