Your are really underestimating Alexander here. Firstly, Alexander didn't just fight the Persians. During his campaigns he encountered and defeated Thracians and Bactrian hill tribes, Greek hoplite armies, Persians, Scythian horse archers (I think Alexander is one of the few generals that successfully countered horse-archers while not employing them himself) and Indians. In other words, he faced every fighting-style of his day, bar the Chinese, and won.
Secondly, the "Persians can't fight" argument is just nonsense. You don't maintain, let alone conquer, a major empire without serious military skills. Yes, Persians fared badly while fighting the Greeks in the latter's home-territory, but equally the Greeks weren't very successful in Persian-held ground. The Athenian reinforcements sent to support the Ionian revolt were annihilated, and the invasion of Egypt, although it got of to a good start, eventually ended in defeat. Ionia remained a contested area until Alexander the Great, which hardly suggests a lack of confidence on the Persian's side.
The Persian weren't just light infantry either: their strike force was their cavalry, and they had some good infantry corpses. That said, they did realise the power of the hoplite phalanx, or else they wouldn't have hired large numbers of Greek mercenaries and formed their own elite hoplite corps.
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