After Alexander died, the Macedonian phalanx and cavalry divided over who should succeed him. The phalanx wanted Alexander’s half-brother, Arrhidaeos, to do so. The cavalry, however, which included Alexander’s most senior officers, were opposed to this. The two sides nearly came to blows before reaching a compromise: Arrhidaeos would become king and Perdiccas, leader of the cavalry faction, his regent (See Diodorus XVIII.2). A few months later, when Alexander’s son, Alexander IV, was born, he was made co-king (See Justin XIII.4).
The peace that this arrangement brought about held for virtually no time at all. After dividing the satrapies of the empire among Alexander’s senior officers, Perdiccas sent Peithon to quell a revolt of Greek settlers in Bactria and Sogdia (Diodorus XVIII.4; see also Dio. XVII.99). Peithon accepted the commission but he did not intend to fight the rebellious settlers; rather, he intended to win them over to his side and take power in Bactria and Sogdia (Diodorus XVIII.7). As it happens, Peithon was foiled in his plan but his was the first act of rebellion by one of Alexander’s commanders, and it set the stage for the conflict that would continue for forty years.
So, that is what happened. But did it need to?
Well, the cavalry could have sent Roxane home and accepted Arrhidaeos as their king, allowing him to rule under the aegis of a regent. In the summer of 323 this didn’t happen because the cavalry knew that Arrhidaeos was unfit to rule: he had a physical or mental impediment that made it impossible. Of course, they did eventually allow it to happen, but when it did, the Wars of the Successors started.
An alternative would have been for Arrhidaeos to be sent home and Roxane’s child, if a boy, to be elevated to the throne, instead. Of course, he too would have required a regent, but only until he came of age.
Or, Alexander’s illegitimate son Heracles could have been made king, instead (Curtius X.6.10-12).
These were the options. Why did the Successors not take them? Or, when they did, why did they not adhere to them?
A mixture of reasons. Arrhidaeos’ mental/physical impediment denied him the authority that he needed to rule. Moreover, it meant that he could never lead from the front, which is what a Macedonian king had to be able to do.
As for Alexander IV, I believe he was rejected out of fear; the Successors feared that when he came of age, Alexander might strip them of the power they had enjoyed for the previous eighteen years, and have them killed.
Why would Alexander IV do this? After all, he would have known that he owed his empire to the Successors. This is true, but the Macedonian political situation in the late fourth century BC was too unstable to permit Alexander IV to trust anyone. He would know full well that as long as the generals lived they would be rivals to his throne. He would not be safe until men of his generation, and therefore men with less authority than him, were in the key positions of power. This is why Alexander the Great removed Philtoas and Parmenion, and I believe it is why Cassander assassinated Alexander IV, and why none of the other Successors so much as said a word about it let alone protested or made war on him. They might not have liked what Cassander had done but they liked the idea of being killed even less.
Heracles was rejected because of old fashioned Macedonian (and Greek) racism: he was seen as a barbarian (Curt.X.6.13-14). Had Ptolemy Lagides got his way, Alexander IV would have been rejected for the same reason.
So, back to the headline question: did the Wars of the Successors need to happen?
When Ptolemy rejected Alexander IV and Heracles, he suggested that the generals should rule the empire together (Curt. X.6.15). I suppose this is why Ptolemy is regarded as a separatist. His idea, though, made sense. It would have lead to a kind-of government of all the talents, just what the diverse empire needed.
The only problem was - fear; the same fear that made Cassander kill Alexander IV. Fear is what drove Macedonian politics. It is the reason why, upon his accession in 336 BC, Alexander the Great killed anyone with a rival claim to the throne; it is the reason he had Philotas and Parmenion killed. I think it is one of the reasons why Hephaestion, Craterus and Coenus colluded in the judicial murder of Philotas (Curt. VI.11.10). In the Macedonian royal court, one was either in favour or out, and one had to do what was necessary to stay in. Co-operation happened but one had to be prepared to betray friends and allies as necessary. After all, they might do the same to you - as necessary.
So, no, the Wars of the Successors didn’t need to happen, but I think that the prejudices of the Successors, allied to their legitimate fears, made the conflict inevitable. The only thing that might have stopped it is if Alexander III had died twenty or more years later and if his son had been as strong and determined a person as his father. But even then, all it would have taken is one cup laced with poison…