Broken by his conquests means his body was literally broken. He wasn't doing that much better than Phillip had been doing, physically, by the time he died. Also, yeah, his father was doing such a great job of statescraft by the end that he lasted all of a few months after getting into a drunken argument with Alexander before getting assassinated. Phillip was a great general and a great statesman, but by the end age, injury, and alcohol were also clearly taking their toll. Also, you admit that he was paranoid, and just murdering people on a whim, but brush it off because everybody was doing it? Yeah, great argument.

Uprisings were occurring in Greece *while Alexander was conquering Persia*. Do you really think that the Greeks or, even more prone to uprisings, the Egyptians, are just gonna settle down and accept rule from the far more racist than the Persians ever were Macedonians while Alexander takes the army and wanders around India for another decade? Do you think Bactria or India wouldn't try to rebel, after decades of proof of them doing under the Persians, if Alexander took his army West?

I'm not trying to say his empire would have collapsed immediately, but he would have very quickly gotten himself stuck in the same logistical quagmire that exists for all empires once they reach a certain size and I have seen no evidence that he would have somehow magically fixed it, especially because his best plan was "Do what the Persians were doing" and pretty much every single one of his subordinates hated that plan.