I'm not sure how survivable Hephasteion's position is after Alexander's death.
You're the royal favourite who's power is based purely on having the King's ear. The king is now dead.
What's to stop one of the other generals eliminating Hephasteion? Especially since they've all had to spend time cultivating their own power bases within the army while Hephasteion will just have ben Alexander's right hand man.
Hm, guess it's debatable how much authority Chiliarch actually gave.
But disregarding that for a moment, historically there were a lot of factors that aided Perdiccas, who Hephasteion would be taking the place of had he still lived.
Firstly, the generals squabbled after Alexander's death but things didn't fall into open warfare until Ptolmey snatched Alexander's body (though cracks were already beginning to appear and the various plotting was going to lead to a flashpoint). Nobody actually died before that except Meleager though. And Cynane technically.
I mean, people are definitely going to be fighting against him, but they'll probably do it openly. On the field of battle after biding their time.
Secondly the mutiny kind of forced everyone's hand. Even if the generals wanted to try and remove Hephasteion from the equation immediately, when the infantry revolted the generals will rally behind him as the commanding officer of the Companion Cavalry. Because the alternative would be a civil war between infantry and cavalry and likely end up with them being lynched by their own soldiers.
So I'm not sure how successful Hephasteion would be in the long run, but he probably wouldn't/couldn't be eliminated immediately. Certainly couldn't do worse than Perdiccas. Plus Roxanne was cool with him right?
With that said, the ability to develop powerbases is an extremely important factor in the civil wars. You could notice that most of the actual diadochi were the people who had been left behind when Alexander marched east or obtained satrapys in areas where it was difficult for their rivals to threaten them. Perdiccas had no homebase he could retreat to and was forced to run around being the fireman for every threat to his power. It's possible (probably likely) Hephasteion would just end up falling into the same mistake if he's regent and then ends up getting shanked by Seleucus.
Course Hephasteion might not have been as heavy handed and alienating as Perdiccas was to his peers.
(I'm keeping the Hephasteion lives scenario seperate from the Alexander lives scenario, for simplicity).
A lot of the army was dedicated to Alexander, especially those of Macedonian stock. If he makes it expressely known that he wants his son to succeed, and that general X is to be his regent, it will be very, very hard for someone to convince the Macedonian core of the army otherwise.
There are numerous examples of kingdoms and empires were succession runs smoothly, hence I'm not as 100% convinced as everyone else that civil war is inevitable after his death. Heck, IOTL, with the shitty succession situatin that we got, there were still people who went to great lengths to ensure stability.
Some things were probably bound to happen. The Lamian War or the eastern mutiny for example. I agree that Alexander's death happened in pretty much the worst way for the empire possible though. Had he remained lucid and kept his decision making ability, things would have gone a lot better.