I'll agree that if Alexander invaded Italy at the start of his career, he would have won. However, Livy is postulating an Alexander who completed his conquest of India. The Magadha Empire (which was right in his path) was an decrepit nation under the Nandas, so let's assume this takes the year it would have taken him to conquer the Indus. Given his track record, he would have then moved south and conquered the princedoms and city-states of the Deccan, so let's say that's another one or two years. It then took him a year to get back from India to Babylon, so that brings us to 323 BC. After spending a year in Babylon tying up loose ends, he invades SE Arabia, and, because he feels like it, Meroe, taking another year. We're now up to 321 BC, the time the battle of Caudine Forks took place. Alexander, however, would first move against Athens and Sparta, for prior slights - both cities, though past their prime, were tough nuts to crack, and that would be another year, which he also spends building up his fleet. By now, 320 BC, he would invade Italy (a relative of his had been killed there sometime ago, so he has a cassus belli). However, it would not be like when Hannibal invaded and built up an anti-Roman alliance. Alexander proved to not care about gaining allies - he invaded the Sogdianans even though they rebelled against Persia and would have been useful allies. His goal, from everything he did, was to rule the world -allies had no place in that belief. He would have conquered Magna Graecia for his kinsman's death, Syracuse to prove himself the better of Athens, the Samnites because they were nothing more than "barbaroi." In short, it would be Rome who builds up a coalition against Alexander, not the other way around. And invading Syracuse would bring Carthage, and its powerful navy, against Alexander. So, in the end, it would still fall down in favor of Rome.