From what I know, Iberia's main barrier to unification and centralization is geography. Sure you have the Pyrenees to the north as a barrier, but then you have all sorts of high hills and literal mountains crisscrossing the country, watersheds that take days of marching through easy-ambush territory to cross, and a kind of polyglot mess of Iberian, Celtiberian, PIE, and Semitic speaking peoples. Any empire would have to either effectively wield somehow or at least loot/sack (easier) the Punic coastal cities, but the leaders of this time didn't really have the kind of civil structure that allowed them to amass large (well, """""large""""") armies for more than a few days without everything falling to hunger and infighting.
Having a highly drilled, almost mechanical military (like the legions) and a sprawling, insidious bureaucracy (like Rome's) and a government that doesn't rely on regional clans/towns/factions for support (like the Republic, see where I'm getting at?) sure help against that geography though. I'm not saying it's impossible, but with weak outside influences not providing a boogeyman to unify behind, I don't see much happening in the long term, really. Sure, one super charismatic Gary Stu (it's happened in history plenty of times) can rise and forge an empire that outlives him by maybe a decade before collapsing. That could happen. But I don't know what else.