You've sort of got your work cut out for you. We know precious little about the CA. There's basically two direct references to it. One is a confusing reference to it in the Digest at 1.5.17, a quotation from Ulpian that states "In orbe romano qui sunt ex constitutione imperatoris antonini cives romani effecti sunt," the precise meaning of which is unclear ("those in the Roman world?" "In the Roman world those who...?"). Then there's Dio 78.9, which states that Caracalla's purpose in instituting the CA was to increase the state's revenues, since taxes on manumission, inheritance, and so on did not apply to non-citizens.

And that's basically it. From these two references and a huge amount of epigraphic data that is devilish to interpret, a massive argument has been made and must be untangled. This is one of the biggest debates currently for Roman legal scholars and scholars of the later Principate, especially since in the past 15 years or so the people who work on this sort of thing have increasingly started to realize the shakiness of a lot of their assumptions. The view that you've repeated above, that the CA was "largely ineffective" at...whatever exactly it was supposed to accomplish (and few people today think we can take Cassius Dio's word for it), is essentially A.N. Sherwin-White's, in his cleverly titled book The Roman Citizenship. Sherwin-White argued that there is little evidence of the CA having a massive impact, and that what evidence there was--mostly epigraphic--suggested that there were few provincials enfranchised in the west, where presumably citizenship was already commonplace, and that in the east, where evidence for CA beneficiaries was much greater, the impact of the franchise was not huge. The major reasoning behind this is that the so-called Aurelii--individuals presumed to be non-citizens who took the name Aurelius after the emperor following their inclusion into the franchise--are vastly more common in the east, and quite sparse in the west. There are many problems with this however. For example, many Aurelii appearing in inscriptions are dated to post-212 when no other means of dating presents itself, on the grounds that Aurelii become common after 212. Likewise, there is no particularly good reason to suppose that the western provinces would have necessarily followed the same naming practices. The best place to look for this is Rizakis' "La diffusion des processus d'adaptation onomastique: les Aurelii dans les provinces orientales de l'Empire." Likewise, Haynes' Blood of the Provinces: The Roman Auxilia and the Making of Provincial Society from Augustus to the Severans is a good place to look, since though it does not focus specifically on the CA it is a vital study for anyone trying to understand how status worked in the provinces. And we're finding that status was not so cut-and-dried as citizen, non-citizen, slave. For example, we don't really understand how municipial grants of citizenship worked, or even necessarily viritane grants. A place to look for this is Gardner, "Making Citizens: The Operation of the Lex Irnitana." We can't even reliably identify citizens from non-citizens, either by using onomastic evidence or by, on the rare occasions when we have this information, identifying their rights, as increasingly we're finding that provincials with citizenship often held "special" sorts of citizenship, which included things like liability to tribute. I mean, we're not even sure how within Italy the distinction between honestiores and humiliores came about, since no law was actually passed that defined these separate categories of Imperial civil law (look at Clifford Ando, Law, Language, and Empire in the Roman Tradition). And then there's the problem of what exactly the CA did. Did it enfranchise all free people in the empire generally? Did it mean that all people within the oikoumene possessed Roman citizenship if they were to move within the bounds within which Roman law could be reliably exercised (since Gargola argues that the Romans, and others in the ancient world, did not really have a concept of limited empire)? Does it mean that all free persons at the time of the CA's institution were citizens? Ralph Mathisen in "Peregrini, Barbari, and Cives Romani: Concepts of Citizenship and the Legal Identity of Barbarians in the Later Roman Empire" has an interesting discussion on the presence within the record post-212 of peregrini, which should in the Republic and earlier Principate mean "foreigner" (i.e. "non-citizen"), which by all rights shouldn't exist if the CA is supposed to make everybody a citizen. Last of all, we're finding that even within the rigid definition of citizenship that Sherwin-White assumed we shouldn't necessarily suppose that low enfranchisement levels were actually the result of the CA even in the west. Lavan has an interesting preliminary report ("The Spread of Roman Citizenship, 14-212 CA: Quantification in the Face of High Uncertainty") which attempts to use a mathematical model (still unpublished) to work out the probable range of citizens in the west in 212.