I think a lot of things depend on exactly how long Alexander lives.
Because if he dies in 314 BC instead, any children of his will still be infants and extremely vulnerable. Like OTL they will become pawns in the great game between successors. Now, if enough potent players feel their interests align with one of his children it may be likelier that one will actually end up being King and surviving into adulthood. But the complication is that these are not the only bits and pieces of the Argead dynasty. There is Phillip III and his wife Eurydice (who was herself an Argead), there is Olympias, there is Alexander's sister and his many other half sisters. Anyone that these sisters marry is going to consider themselves party to the equation, and their children will be regarded as Argeads too. Now these things are not insurmountable, but anything that imagines an actual Argead Empire arising out of Alexander dying around this time will need to take account of all of these pieces.
However, at the other end of the scale you can potentially have Alexander living to a reasonably old age. This might not be a likely option, but it is in theory possible. In this particular case, Alexander can do an Augustus and simply outlive both the previous and his own generation. This would leave his Empire in the situation of being unable to remember a time before Alexander; in this case, Macedonian tradition wouldn't exactly be an issue if no-one was alive who remembered or cared about it. That isn't a panacea solution, there would still be problems. Legions of problems. But it leaves a lot of time for problematic characters to be dealt with or to die of natural causes. Because if Alexander instead lived to 60-70 years old, say, then that's probably all of the Diadochii of OTL dead by that point along with Olympias and a number of other important figures. Alexander dying in 286 BC, say, does make a difference to the equation. If the dominant generation is the one that grew up under Alexander instead of beside him, that does alter things significantly; because as it stands, OTL left a number of talented and ambitious individuals being shown what an individual with willpower and military acumen could achieve and also left them in positions of power in an unstable situation.
However, even with an octogenerian Alexander his death would probably still result in a number of problems; even if he became a dedicated administrator he would almost certainly have put in place a number of solutions that caused his successor problems. After all, Phillip II did exactly that to Alexander; he was an extremely intelligent political animal but his polygamy left Alexander with both a bad example and a host of potential dynastic rivals. For example, say Alexander tries to bridge the distance between Macedon and Mesopotamia by appointing someone King of Macedon with the assumption that Alexander outranks him as King of Kings. That might work during Alexander's lifetime. But upon his death, that client king is likely to become extremely ambitious given how distant they are from the political centre of the Empire. And if they're an Argead they have a potential claim to the big-time league as King of Kings. Someone with military talent can march, with Macedonian armies, from Pella to Babylon and take over the Empire; after all, that's exactly what Alexander did to the Persians.
I think the best case scenario without assuming extraordinary luck is this. Alexander lives long enough that one of his sons is able to survive into adulthood at least, and that son is appointed co-regent. Many of the key OTL diadochii figures will likely have already died, or fallen out of favour, by this point. But the Empire is still going to pull at the seams; either satrapies still won't have been properly integrated into the centre, or they will have been partially decentralised and will seize their chance to get out of the arrangement. And if Alexander kept the administration of the Empire roughly the same as the Achaemenid Empire his successor inherits all of the problems that system had; overly powerful satraps, a reliance on military power to guaranteee stability, and having too many potent figures in competition with one another and disagreeing with one another due to power politics. There's also a huge question mark over what would have happened with Chandragupta, who was already born by the time Alexander conquered the Indus region and is thus going to be a thing during Alexander's lifetime; the situation in the Indus is likely to be even less stable than in the Seleucid equivalent, as Seleucus did attempt to shore up the situation there (and was still ultimately unsuccessful). And Greece is still an enormous drain on military manpower for an Empire whose political centre is in Mesopotamia. That might be alleviated by similar settlement policies to the OTL Seleucid ones, but if we take our surviving accounts at our word he preferred to exclusively colonise with Macedonians and natives and fundamentally distrusted Greek troops and Greek colonists so that might be somewhat out of character. Though the thought occurs that a Greek rebellion might be punished with mass resettlement, in the ancient tradition of Near Eastern Empires. That might take much of the sting out of Greece, but would require the situation to deteriorate in Greece in the first place.
In other words, even with a long-lived Alexander I put an enormous question mark over Macedon, Greece and the Indus region at the very least.