Good morning, hope life is treating you well.

First of all, it's important to understand that Alexander wasn't simply facing a numerically superior land force; the Persian fleet, helmed with a number of Phonecian sailors, was vast. This made his invasion more complex than simply knocking over the dominoes of successive cities en route to Persepolis.

Alexander raised a fleet as Hegemon of the Corinthian League to protect his supply lines [Fox, 2004, p153]. However, directly challenging the Persian fleet would have been a difficult task, in and of itself. Therefore Alexander's route and immediate conquests were aimed not only at slowly toppling Achaemenid aligned cities, but in starving the Persian fleet of a sufficient port [Arr. Anab. I.18.1, I.20.3]. The seige of Tyre and capture of Egypt satisfied this objective [Adcock, 1997, p46; Engels, 1980, p34], and were you to look at a map display a clear deviation from a direct trek to Persepolis.

Alexander was also, arguably, innovative in his ability to undertake and complete seiges. [Arrian, II; Heckel & Yardley, 2004, xvii.]. Again, this was important in securing the Eastern Mediterranean, as well as supply line and flanks. Achaemenid strength lay in its ability to field large armies and a wide variety of cavalry. Long protracted sieges weren't in its interest. As a result, Alexander and Darius III were essentially hunting for a showdown. Alexander needed it as it was the objective of the Hellenic League of which he was head [Roebuck, 1948, p90-92], and Darius to secure his legitimacy as a capable military leader [Briant, 2002, p90; Curt. X.1.31; Wood 1997, p47], and his border, against a foreign invader.

Although Alexander would go on to be more militarily independent, outside of support from the Greek poleis, he was dependent upon the Greeks for man power and home stability prior to the Battle of Gaugamela [Cartledge, 2004, p176]. To legitimise his position as Hegemon he had to be seen to be avenging the ills of the Persian invasion of mainland Greece the century before. Simply capturing cities would not do. He had to defeat Darius, whom he had already rebuffed when offered a peace settlement and the hand of one of the latter's daughters.

Persepolis would go on to become a complex issue; burnt perhaps as punishment for the destruction of the Athenjan Acropolis, a drunk accident, or a means of stripping the Persians of a central ceremonial capital.