@Galba Otho Vitelius
I agree with some points, but a few counters or concurrent thoughts regarding some of what you mentioned.
1. I would not be so quick to assume that the Persian Empire lacked a counter to the Phalanx or generalized heavy infantry warfare. In the first conflicts between the Achaemenid forces and Alexander, the Persian forces nearly carried the day, most certainly. Had the Achaemenid imperial armies would have fared better had they faced poorer generals that followed your line of thought and assumed super heavy phalanxes were superior to their enemies and subsequently would have been routed or could have been much more easily. Alexander and more skilled Hellenic generals understood the importance of a combined arms in their warfare, utilizing light cavalry, elephants, archers, slingers and many other units to better support their phalanx lines and resist engulfment. It also is not necessarily a weakness of martial skill alone regarding the Achaemenids.
When we discuss the geopolitical results of certain conflicts, we always must remind ourselves that in the case of major empires, such as the Achaemenids, though they have vast resources, populaces and so forth, they also have expansive borders, frontiers, unlimited enemies and are disliked as hegemon. Empires such as these, require to station out their armies across vast lands, appease a massive number of people, protect every piece of land lest they lose respect and maintain a diverse set of imperial initiatives. They in essence, lack the initiative and the drive, not necessarily in a spiritual sense, but in materialistic sense that their size, structure and format cannot contain it at the moment, even with great visionary leaders. Meanwhile, states who are strong and smaller on the exterior of said empire, have all the benefits of power but none of its weaknesses and are much more ready to counter the large and weakening empire if need be.
There is also the point that the Achaemenid structure is perhaps an inferior system compared to later iterations and even its predecessors in terms of engendering an imperial complex that could weather martial conquest. One major weakness, is the Achaemenids, unlike their successors, the Seleucids, Arsacids and Sassanids, might have lacked a certain decentralized defense mechanism. By this, I refer to a way to perpetuate the dynastic or political agenda without the imperial army personally. In the Arsacid empire, their empire tended to be hemmed in from all sides at a near constant basis and despite emperors falling in battle, losing miserably and followed by a civil war that erupted immediately after, the Arsacid polity continued to endure and recover rapidly. Even in the last days of the Arsacid empire, the civil war between Artabanus IV and Vologases VI, the Arsacids were able to recover border areas lost to the Romans and defeated the Romans at Nisbis and seemed to be doing well should the civil war end. Had it not been for the incredible victory of Ardashir I over Artabanus IV (what at the time to many of the noble houses, must have been a fluke of monumental proportions), the Arsacids would most likely have endured the civil war and launched another counter against the Kushan and Romans who harried their flanks.
Sassanian imperial durability was similar. At may moments, the empire seemed to be in a situation far more grave than that of the Achaemenid crisis. The Hepthalite invasions was one such crisis that threatened the entire fabric of the system. Sassanid imperial armies were defeated in 484 under Peroz I and he was slain. The noble houses rallied together despite this and defeated the Hepthalite invasion and restored the Sassanian throne. Likewise, despite recent conflict between the nobles and the monarch, the Sassanian state was able to gather nobles to defeat the Gokturk invasion in the 580s. When rebellion from the Mihranid Bahram Chobin occurred, despite the tyranny, hostility and bloodlust of the emperor Hormizd IV, the Surenid noble house in launched a palace coup and instead of proclaiming a new polity, simply put a new Sassanian emperor on the throne and requested peace with the Mihranid clan rebels. To add, the Sassanian throne was able to then return to power, due greatly to much of the existing Dahae-Parthian nobles remaining unwilling to accept a new dynasty. The Achaemenid's lacked any of this sort of mechanism that would allow it to remain in power no matter the circumstances. Much of this, is that they lacked the robust dynastic nobility of the later Iranian empires.
Additionally, we may add that the trope is typically a story that the Achaemenid's aside from a few rulers, were known to rule through a positive patronage. That is, they treated their subjects well and gifted them varied liberties and autonomy and required only submission in a weak sense. This is positive for when you can defeat all external enemies. Yet it could become negative, if your rule is engendered only through friendship, as these things tend to be transient, especially when you lose two major battles in a row and are a massive empire. This is why when Alexander swept through the empire, most of the states simply reached agreements with Alexander and joined him, aside from Tyre, the far east and the Indus Valley states. Assyria certainly, for all of its mayhem and devastation, was a more durable empire generally than the Achaemenid. Assyrian policy neared the point of bringing terror and trembling, even to its allies and reminding its friends of the results of treachery. This meant that when the Assyrian empire was in complete and total disaster, the likes of which the Achaemenids had not tasted until its final days, Assyria was still able to fight viciously for at least 7 years (in just the small area of Assyria proper [the rest of Mesopotamia had fallen]!) and even in this weak stance, the Assyrian empire was still being supported by a myriad of vassals across the Levant and its large vassal of Egypt. Assyria brought fear to the post-Bronze Age Middle East, but this also allowed a greater stability for trade and their armies made many states comfortable and the idea that Assyria could lose a war and not recover just 20 years later, as they had done in the past, might have seemed impossible to the people of the time. It is most clear to us, that the same cannot be said of the Achaemenid empire.
2. If a continued Achaemenid empire occurs, they will eventually have to run into the inevitable road of their actions in Central Asia. Their prior two century expansion into the steppe had, alongside activities in China, had created the precedent for the creation of the first steppe empire, in the Xiongnu. This will become a massive issue for the Achaemenids as the steppes will churn more and more in the coming years and will spell great calamities if the Achaemenids do not prepare their eastern defenses. In otl, much of this expansion in the early phases, were curbed by the role the Seleucids and their Greek vassals, who played a role in constructing free cities across the east with large slave trading operations, militias and large walls which repelled the earliest rumblings from the Saka and other steppe peoples. In later times, the Greek state in Bactria aligned to the steppe Dahae (Arsacids) and conquered the Seleucid empire's eastern lands, who had overextended herself in the wars of the successors. Later, not even the Bactrian free cities, armies and Arsacid alliance were enough to quell the expansion of nomads from the north and east.