Why would the Romans reject a wealthy city as a province? If there's no insurrection, a Roman garrison is keeping the peace, and most importantly they are paying taxes, what is the problem. In this scenario an intact Carthage has been added to the empire. I think this is the only likely scenario out of the three presented in the OP. An independent Carthage would always be a threat and another war would happen. Satellite kingdoms did not last long in the Roman sphere, they were fully incorporated or too distant to maintain the relationship and Carthage is not too distant.
Alexandria, Antiochia, Athens and a myriad of other cities were rich as well
Athens was not a rich city by that point, not politically important. Athens was a prestigious city famous for its schools and philosophy. The city had no political power whatsover and was treated like Florence was treated by the 18th century noblemen in their Grand Tour.
Antioch and Alexandria posed no ideological challenges to Rome. They were absolute monarchies.
Instead, the 2nd century Carthage had an inclusive political system. A political system much more republican and inclusive of the roman one. A trading city spreads its ideological influence, especially if it is big, prosperous and close by. Remember Cato's carthaginian figs? He brandished fresh figs to show how close Carthage was. Proximity of an ideological enemy of the senatorial class was the main threat. If Carthage was reduced to an inland city ruled by a limited landed aristocracy, then it would not have been a threat.
Lastly, have in mind the period we are talking about: the mid 2nd century, when the senatorial class had reasonable fears of popular dissent. The other city that was destroyed was the rich commercial city of Corinth, again with an inclusive political system. And war came to the Achaean League when democratic leaders rose to power and presented an ideological rather than military threat to Rome. Even so, the commercial center was destroyed: not Megalopolis up in the mountains nor Argos with its agricultural economy.
The Third Carthaginian and Achaean Wars were not wars for military supremacy nor were based on fears regarding the future security of the Roman State: They were ideological wars because the senatorial class hated inclusive political systems and was hungry for plunder. Even with that kind of responce, the social crisis they were afraid of, was just postponed.