Well I would disagree with the assertion that Carthage's generalship was notably poorer than that of the other ancient great powers. The Sicilian wars went pretty well for Carthage, by the time of the First Punic war there was talk that Carthage would soon finally take control of the entire Island (although the credibility of this belief is another debate entirely). The Carthaginians suffered some defeats in the wars against Sicily of course, but they won just as many victories. The Mercenary war was brutal but Carthage won that conflict as well, pretty convincingly.

I do think there are a few problems with your statement/opinion. Firstly its looking at a period in which Carthage faced one main enemy, that being Rome. Rome became the preeminent Mediterranean power for a reason, they were very good at winning wars. The Hellenistic Kings look like pretty shitty generals if we simply focus on their conflicts against Rome, yet Philip V of Macedon and Antiochus III of the Seleucids were both noted to be good generals. Rome was a state very good at warfare, with a system that produced reasonably good armies and reasonably good generals in massive numbers. To Quote Adrian Goldsworthy, the Roman system 'allowed the Romans to consistently raise average armies led by average generals, whereas Carthage had poor armies led by average generals, or average armies led by poor generals'.

This is not to excuse bad Punic generalship. The performance of the all the Carthaginian commanders who don't have the surname Barca was abysmal, particularly the Carthaginian generalship in Sicily. However the Punic generalship in the Third war was pretty good, all of the Barcids were reasonably able generals, although certainly Hannibal and his father were far greater than his brothers. The fact is the Romans won most of their wars, and if your on the losing side of a war, your probably gonna lose more battles than you won.

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Secondly I think this focuses too much on Carthaginian defeats. Again if we look at Rome during this period and only look at their defeats they look terrible. I think this is in part due to the problem that we have no Punic sources, and therefore much of our information on their conflicts comes from Rome, and there is little focus on conflicts outside those with Rome or to a lesser extent Sicily. However during this period Carthage had continued military success against the Numidians, crushed the Mercenary revolt, and conquered much of Spain. They can't have been too bad to have this much success.

On the other hand, an explanation for some of the leadership faults of the Carthaginian generalship can be placed upon the army. Now this isn't in terms of the quality of troops. The quality of the Carthaginian soldiers were generally exceptionally high. They could hire a vast number of different specialist troops and the troops they did hire proved their quality time and again. The Punic skirmishers and cavalry time and again beat their Roman counterparts, they had elephants, the Libyan foot was very well trained and disciplined, and capable of advanced maneuvers, while the Gallic and Spanish were ferocious close combat warriors. However all of these people spoke different languages, there was no standard unit size between these troops, most had never fought with troops like their counterparts before. This meant that it took a long time to train a Carthaginian army into a proper army. You'll often see in historical accounts of Carthaginian armies that are newly raised, one section of the force will perform very well, but the army proves unable to exploit this because it doesn't have that connective tissue that forms the disparate parts into an army. This obviously first of all that while Carthaginian armies once given time can perform extremely well, and accomplish things their Roman and Greek counterparts weren't capable of (see Hannibal, Hamilcar, Mettones etc), it also meant that newly raised Punic armies were not generally capable of very advanced battle tactics, although this is not something unique to Punic armies.

As Goldsworthy points out this lead to a very defensive and tentative command from most Punic generals, unwilling to risk the valuable asset that was an experienced and well trained Carthaginian army. Rome won its war with Carthage partially because its generals were continuously aggressive and continuously took the initiative, while this caused some disasters, initiative also brings victory.

I feel my answer here is incomplete, but I need a bit more detail to answer your question fully. Can you point to the amateur levels of military command from the Punic generals in comparison to the Greeks or Romans/Persians etc? And what do you mean by the Carthaginians seemed unable to change their approach unlike the Hellenistic Kingdoms/Greek states/ Romans etc?

Sources:

Adrian Goldsworthy Fall of Carthage

John F. Lazenby The Hannibalic War

Nigel Bagnall The Second Punic War

Dexter Hoyos Mastering the West Rome and Carthage at War

Polybius The Histories

Livy The history of Rome