This question gets asked here a lot; the most recent one I saw was just yesterday. I answered it a while ago here.

It's important to bear in mind that historical states and powers don't just appear out of thin air with a set amount of troops and resources and a free choice of how to use them, like the first turn of a computer game. They arise as the outcome of historical processes and their rulers' actions are guided by historical forces. Towards the end of his life, Alexander is said to have contemplated going south and west to conquer Arabia and Carthage, but this was only after the traditional nemesis of the Greeks, and the largest and richest empire on Earth, had been subdued.

It's also important to bear in mind that Alexander's entire 12-year reign was essentially consumed by a single continuous military campaign. He wasn't able to just put the conquest of Persia on hold to turn west for a bit. He was effectively path-dependent on his way East until his soldiers mutinied in India, and by the time he was back in Babylon and ready to start a new expedition, he died.