In the OTL conflict with Rome, how much of the outcome came down to population? I've got the impression that relative to Romans and Greeks, the Carthaginians had rather slowly growing, relatively stable populations, and that their method of gaining influence and wealth was mainly a matter of scouting out the existing power base in a region, making contact with whoever either ruled or was in a position to rule with a little bit of help and guidance, and, playing kingmaker as necessary, form a trading relationship with this local power. They sailed far, but settled very lightly, not disrupting the local relationships much, and spun a rather gossamer web of trade over very long ranges. The Greeks on the other hand, when colonists arrived somewhere, intended to take over everything in sight for themselves; this meant inevitable conflict but they'd generally win through high concentrations of force, and then having established a colony they'd expand it until limits of physical transport and regional carrying capacity were reached, thereupon beginning to accumulate people for a new colony. In the interim as regional opportunities for getting rich individually were preempted by those who got to the good land first, they became traders, functioning as the scouts who would choose a new territory to colonize. The Roman variation on this theme was that they were a local tribal power who resolved the conflicts they had with their neighbors by subjugating them and then incorporating them into a larger system that somehow remained focused on Rome as it expanded. But expansion meant larger and larger (spread over larger areas) populations of classes suitable for recruitment into the evolving legions; during the expansion of the Republic Roman armies were composed mainly of people who identified as Romans and served not primarily for pay (though it was of course essential that legionaries did get their pay) but because it was their duty as Romans to serve; in return they looked forward to getting land of their own in a Roman town.
Now these are impressions I have; I don't know whether any of what I have said thus far can be readily disproved or not. We suffer from a lack of information. Most of what we think we know about Carthage comes from fragments of writings about them that have survived, written entirely by their various enemies. Thus a classical work that conveys much detail about how Carthaginian politics worked is probably largely accurate but may contain some misunderstandings, there either by honest mistake or for propagandistic reasons. At this point, only archaeology can supplement these scanty sources, and we have a lot of blanks to fill in with speculation.
I've noticed when trying to find out more about any ancient society the huge gaps in knowledge we have. As a modern person influenced strongly by materialistic historical philosophy I assume that demographics is hugely important--just how many people, packed in how densely, contributed what sort of material production at what level of productivity to a given region? How much of the net productivity of the regions that the Carthaginians traded over was available as transferable wealth they could appropriate, and how economical was it to transfer these goods elsewhere in their sphere to be traded at what rate for what other goods, and so how much material wealth stuck to the fingers of the Punic middlemen? It is often stated that a huge weakness of Carthage relative to Rome, or even to prior rivals such as the Greeks, is that her armies were hired mercenaries. That's not so bad if the wealth available to hire them is fabulous though it does raise that infamous Roman question, "who shall watch the watchers?"--if Carthage could hire armies comparable to what a tyrant of half of Sicily or the Roman Republic could muster, what stops these professional soldiers from taking over Carthage itself and running it their way? Are suitable armies even available for hire?
And just why and how should a Classical era people such as the Punics differ dramatically from the Greeks or Romans in their attitudes and demographic patterns anyway? Did the Punics have a low rate of population growth, and if so, why? Were they more like the Greeks than I think, except they had reached their demographic limits in North Africa--and if so, why not colonize Iberia or even Italy? Because there were already Greek colonies in the way in Italy by the time a desire for new colonies would arise in Carthage? OK, but there are the various Mediterranean islands the Greeks didn't do much with, and of course a lot more North African coastland to the west, as well as Iberian shores. Why did the Carthaginians not preempt the Romans there by many centuries?
So to repeat, what it looks like to me is that somehow, the Carthaginians had a relatively slow rate of growth and tended to regard a rather small region of North Africa as their natural and adequate homeland, and all the people they sent out intended to return there. They augmented their limited numbers with hired forces of various kinds to assist them in far-flung operations, and then returned home to enjoy wealth and status in accordance with mercantile gain. In so doing they spread a broad but thin net--so thin apparently that even on vital and nearby Sicily they contented themselves with a few strongholds leaving the rest of the island open to ambitious Greek settlements that for whatever reason they did not stop and which grew into pesky threats that they could not later eradicate.
Now if nearby and obviously valuable Sicily was not tightly controlled and thoroughly Punicized before the Greeks showed up, why should be expect Carthage to be able to set up stronger and denser colonies in distant Iberia?
I suspect that the Baracid ability to do this later had to do with changes in Carthaginian society, very likely in reaction to the threats and challenges posed by the Greeks and Romans.
Was there in fact, as I am wildly speculating, some sort of demographic deficit in Carthaginian society relative to Greek and Roman patterns? If there was, I might suspect that at the basis might lie degrees of patriarchy. A high birth rate takes a toll on the women of any society; the more polarized gender roles are along the familiar-to-us axis of typical modern patriarchy (by modern here I mean prior to relatively recent waves of feminism at various levels of society) the more society can demand of its women that they produce lots of offspring even if conditions are such that most of these babies die young. The upshot is limiting the roles of women in acknowledged public business and a high death and disability rate among them. Was it the case that Punic society, at least as it evolved in Carthaginian north Africa, allowed women more autonomy and respect, and did this cause a low birthrate that constrained these Punics to have the sort of far-flung but soft pattern of hegemony I speculated on? Classical Greeks certainly tended toward a possessive and authoritarian handling of respectable women, and the exemplary legends of the Roman Republic stressed the duties and submission of proper Roman maidens and matrons--so was the ultimate steamrollering of Carthage due to the more rampant misogyny of Greek and Roman societies, with associated militarism?
Do we have any data at all on these points or am I free to speculate widely--and pointlessly?
Anyway perhaps the Baracids drew from a new and rising faction of Carthaginian society that was belatedly able to colonize on Greek lines and consolidate regional control in Roman fashion, perhaps with that front-line warrior family having learned lessons from the peoples they fought against or side-by-side with as allies. Or conceivably, the Romans were the ones who learned some crucial lessons from Baracid inventions in policy, and having assimilated them and turned the tables later, chauvinistically failed to acknowledge the hated Punics as their teachers.
We know so little, I fear, it would be hard to say definitively why Carthage did not establish an iron grip many centuries before latter-day rivals showed up to plunder in their turn. In early days, the Punics might not have Greeks to worry about and the Romans were a single village, but the Etruscans are often mentioned in Western Mediterranean town histories as early actors on the scene, maybe the Etruscans were stronger than we now realize and displaced the Punics successfully before falling to Rome in their turn?
I suspect though, in view of the light hand that gripped Sicily, that for whatever reason--the relative power of women in society perhaps, or the scanty agricultural returns of their North African base, or a focus on merchant activity inhibiting and distracting from a focus on military capability, whatever--Carthage colonizing Iberia much earlier than the Baracids did, to similar levels of density and development, was simply not in the cards.