Pytheus: Why did Alexander not divide his army--simple it numbered less than 60,000 at its apex with only <10% cavalry. Genghis Khan could and did command armies exceeding 100,000 and later in his career could delegate multiple subordinates each commanding 50,000 to various objectives. Furthermore the Mongols were exclusively cavalry. As a general rule of thumb infantry must be concentrated to be effective; cavalry not necessarily.
I hate to tell you there was no Carthage to conquer at the time and he did in fact invade India, winning the last major battle of his career. His men finally laid down the law and refused to go further east.
As to an appreciation of his Strategy/Grand Strategy I recommend Liddell Hart's STRATEGY . But regarding tactics Greek/Macedonian culture absolutely required a personal touch. The commander had to be there.
He not only had to lead but had to be seen leading.
Paranoid? Come on. Given the fact that he came to the throne due to the assassination of his father, an assassination in which either he or his mother were quite likely responsible, it would behoove him to be reasonably wary at all times. When the votes are counted and Clinton beats Trump or vice versa neither one worries about the other having him killed. Don't use modern values to judge him.
Medenaywe: the word is conquer. Unlike today there was no reason to find a reason other than I want what you got and I'm taking it.
AlphaS520: I recommend Liddell Hart to you also for an appreciation of Alexander's genius. He won every battle he ever fought. Always facing superior numbers; always triumphant. And even to suggest that he lost to Porus goes against ALL the available evidence.
Lastly, what's wrong with slaughtering all the inhabitants of Tyre. Not only was that the practice of the time ie., any city that is taken by storm is liable to indiscriminate slaughter, BUT the practice continued into the 19th century as witness the taking of the Alamo by Santa Anna.