Well, the Carthaginians would presumably have to conquer their empire themselves in order to conscript others into their armies. And even once they had, having to keep a large portion of their manpower at home to keep the serfs in line would limit their strategic possibilities (and, arguably, defeat the main point of having a professional citizen army in the first place -- why bother when you can't ever use it?). Not to mention, it would make them more vulnerable to invasion of their homeland. The comparison between Rome and Sparta is instructive here: even during the darkest day of the Hannibalic War, Rome's allies largely remained loyal to them; on the other hand, when Epaminondas invaded Laconia after the Battle of Leuctra, the helots all deserted to him and Sparta never really recovered.
The Spartan model isn't necessarily a standing army, rather it's a large cadre of leaders for armies fleshed out by allies and mercenaries; they wanted to expose their citizen class to as little direct danger as possible, so often the only Spartiates in an army were the commander and about thirty officers. This was enough to greatly improve the fighting power of the rank and file who lacked Sparta's lifelong training regimen. Being able to successfully integrate Gauls, Iberians, Italians, Greeks, and Africans into a cohesive, disciplined army under a caste of Punic professionals could be a major advantage, given the less-professional Italians they fought against.
From what I can tell, most ancient empires had to deal with servile revolts, so it's hardly a unique disadvantage to a class of landed officers. It's also largely unrelated to the fastness of allies; all Mediterranean empires had large classes of brutally mistreated slaves, and for what it's worth, most of Italy outside Latinum did defect to Hannibal; Samnium, Apuila, Magna Graecia, Cisalpine Gaul. Capua, second only to Rome itself, joined his camp.