1. it wasn't Alexander's choice, he completed Phillip's planned invasion of Asia Minor, and it went better than expected at Granicus, so he kept going.

I feel the notion of revenge for the Persian invasion was a nice motivator and pretext to keep Greek allies onside. It was a fairly unrealistic goal, but if it gave Macedon and her allies enough steam to take Asia minor, well and good. Phillip was a very pragmatic and realistic leader, for all his ability and ambition I don't think he was setting out to replace teh great King, just push him back.

Alexander was a nutjob though, possibly believed all the hype and certainly acted like it was true.

2. After Issus it became apparent that the western half of the Persian Empire (basically the Mediterranean littoral) was Alexander'ss for the taking, so he took it. That secured, the rest of Persia's dominions were available, at the price of a battle: Gaugemela.

3. After Gaugemela he sacked Persepolis which was Operation Persian Revenge's "mission accomplished" moment. Alexander's new mission became "re-found the Persian Empire".

Persia's Empire falls into two halves in my mind: the wealthy provinces of the west (Mesopotamia, Syria, Egypt, Lydia) with alien locals ruled by Persian satraps and the Arian or Iranian east, peoples with more in common with persia and less apt to conquest by non-Iranians. I think the Western Provinces had bene fought over and pacified multiple times and knew how to bend the knee, but less subjegated (or civilised?) folk made a better fist of resistance (eg Hellas, Iran).

Alexander fought three major battles and some sieges in the Western Persian Empire, but in the East he had to skirmish and fight and siege his way from Parthia to India.

So half the empire fell in 3 years, and the other half took seven years, and fratured and revolted to Iranian rule many times under the Macedonians.

I feel italy Spain and the rest of Euriope were of the same type of cultures, unpacified, hard to unite (even for a local), hard to hold onto once conquered. Thrace fell from macedonian hands faster than Egypt or any of theuir Eastern conquests.

Likewise the Romans sprinkled Italy with their blood for 300 or more years to bring it to heel (perhaps the Social War being the true pacification), Spain took 200 years of plodding slaughter. Gaul resisted conquest for a long time although perhaps they softened themselves to rule ("The Time of Soldiers"): certanly the Germans did not, despite being poorer and less united.