I don't think this premise is true? This is more /u/LegalAction's territory than mine, but there was basically one big conflict over citizenship in Roman history, and other than that the Romans didn't really have a problem with extending the franchise to foreign peoples, albeit not necessarily at a particularly fast rate, and not necessarily evenly. The big conflict was that starting in the late second century, when C. Gracchus first seriously proposed enfranchising all the Italian allies that had not yet been admitted to citizenship yet. We find some talk about this a little earlier in the sources, but C. Gracchus seems to have been the first to make it a really important point.

But the background of Gracchus' proposal should be examined here. Prior to about the middle of the second century, the Romans regularly distributed land seized from enemies in war, which was called public land. Basically, when the Romans captured enemy territory they established colonies, fortified citizen towns that served as military outposts. The rest of the captured land, most of which was rural, was divided into centuriated plots of a couple jugera, the minimum amount considered necessary to allow a soldier to equip himself, and these plots were granted by Roman citizens who were settled there. This had two benefits. First, it ensured that the maximum amount of the population could be included in the army's manpower. Second, since captured land tended to be along the frontier it created a densely populated militarized frontier, settled by experienced soldiers and their descendants, and reinforced by fortified colonies that could serve as a network of outposts. Any remaining land was considered public land, which often existed between Roman communities and Italian ones. Often this could be used to police foreign peoples, as at Genoa and Capua, where former Roman enemies were either ringed in by public land that they had to request access to or were cut off from their most important pasture land, and thus had to rely on Roman permission to maintain their livelihood.

By 133, when Ti. Gracchus proposed his land law, the Romans had not founded any substantial colonies in a couple generations (something like 50 years), and had not distributed any public land in the same time. Moreover, Rome's most important wars in the period were being fought outside Italy, in Spain, the east, and in Africa, where the citizen population could not benefit from land seizures. The Gracchan land law was intended to solve the perceived manpower problem resulting from this. But it was symptomatic of greater tensions throughout Italy, and ten years later when C. Gracchus was tribune the conflict between Roman citizens and the Italian allies that had roots going back at least a couple decades started to come to the fore. One part of the problem here, presumably, was that during the same period that the Romans weren't founding colonies in Italy they also weren't incorporating Italian communities into the franchise. Roman colonial foundations weren't simply military occupation. The foreign population around a colony was quite frequently granted citizenship and incorporated into the Roman state. In particular, crucial Roman allies, especially tribal and decentralized peoples along the Apennines that provided crucial manpower to the army and were considered to be especially high quality recruits, were typically enfranchised as entire communities. That's how the Marsi tribe (famously considered the best soldiers in Italy), the Marrucimi tribe, the Frentani tribe, and others in eastern central Italy were admitted to the franchise. Usually a Roman colony was founded in their territory to police them, but most of these cultures were highly decentralized in any case. In other areas, most notably in Gaul along the Po, the foundation of Roman colonies in captured territory slowly extended Roman citizenship into the surrounding population even when the nearby land hadn't been distributed to Roman citizens. By the middle of the first century the population density of Roman citizens along the Po was quite high, and of course the entirety of the population of Cisalpine Gaul was eventually admitted to citizenship in the 40s, after an earlier law a couple decades before that had extended it to the Cispadanes, or those living south of the Po.

The sources make it pretty clear that the resistance to the mass enfranchisement of all Italians that hadn't already been admitted to the citizenship was mostly due to the massive influx of new citizens that would result. Prior to this, while the Romans had fairly regularly extended the franchise to Italian populations for various reasons and services rendered, they weren't particularly fast or systematic about it. I suspect that a lot of these communities, especially like the Samnite towns in the south, had probably been languishing for some time, although /u/LegalAction knows more about that kind of thing than I do. The point is that whereas earlier Italian citizenship had been a pretty manageable flow, Gracchus and the later tribunes who proposed the same measure were suggesting to open it into a flood.

Theoretically this shouldn't really be a problem, but the sources indicate that the friction was based on elections and voting. In particular the tribal and plebeian assemblies, those that elected the lower magistrates, the tribunes, and the military officers, and that passed laws and judged the highest crimes against the state, were organized along tribal lines. All Roman citizens were assigned to (at least nominally) geographically based voting districts, called tribes. Lily Ross Taylor showed that these were organized according to a radial structure (actually a couple radials), in which land pointing in certain directions was assigned to certain tribes as the Roman frontier expanded. This meant that by Gracchus' time some tribes had grown massively at the expense of others (and C. tried to fix this by assigning new colonies to underrepresented tribes), but more importantly it means that whenever an Italian community was granted citizenship it needed to be fit into that tribal scheme. This had the potential to affect voting massively--famously, the four urban tribes were massively overpopulated (and further bloated by the assignment of all freedpersons to these tribes) considering that they only had one vote each, the same as each other voting tribe. The fear, our sources (especially Appian) tell us, was that if the new citizens were distributed evenly into all the tribes they would outnumber those who already had their citizenship, and render their votes less important.

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