Sadly, the common view is a classic case of misdirected assumptions. But now, here are the facts.
The NT cites the name "Erastus" three times: Acts 19:22, Rom 16:23, 2 Tim 4:20. The man in Acts is being sent by Paul into Macedonia, alongside Timothy. The man in 2 Tim is being left behind by Paul at Corinth. The man in Romans is sitting with Paul in Achaia, sending greetings. In order to equate any two of these three named persons, we've got to have good reasons for doing so. And for two of the three, we very much do have those reasons.
It makes sense to identify the Erastus of Acts with the Erastus of 2nd Timothy; as a traveling companion of Paul, seemingly even a junior apostle-in-training. He's being sent somewhere, he's remaining behind somewhere, he's traveling alongside Timothy and being utilized by Paul much as Timothy often was utilized. That all fits, quite reasonably, and the historical interpretation of both references in tandem can even provide a fuller picture of who this Erastus might have been than could any sum of the two separate readings. Please note, this is both positive, helpful and normal, for historical method.
The problem only comes in with the reference in Romans.
The traditional identification of this man with the Erastus of Romans rests on three fallacious bits of reasoning: (1) that the name is enough, (2) that Paul wrote Romans from Corinth, (3) that Erastus must therefore have been the city-manager of Corinth, and that this parallels the 2 Tim reference. To each, now, in turn:
On the first point, I'm speaking more about pulpiteers than scholars, although it's shocking how often, how quickly and how uncritically some credentialed commentators still equate all three names. Certainly, without the same name we wouldn't even be having this conversation, so evidently they must give that some weight.
On the second point, Acts 20: 2-3 only offers that Paul wrote Romans from southern Grece (Achaia). It does not say Corinth. We cannot even assume that Paul walked into Corinth on that trip, because we don't know if the church in Corinth was still welcoming to him at that point (2nd Cor 12:20ff), let alone that the church there was still gathering. Paul may not have stayed in that city long enough to shake the dust from his shoes, let alone write a masterpiece such as Romans. But even with all those necessary doubts to one side, one thing we do know is that Phoebe, the letter-carrier, was from Cenchrea. Phoebe was not from Corinth. This (at least) suggests that Paul more likely wrote from Cenchrea, a town roughly 7 miles east of Corinthian gates.
On the third point, the Erastus with Paul in Achaia doesn't have to have been a city manager currently. It could easily have been a job the man held at some point, but a title by which his friends continued to call him. Thus, if this Erastus were to be identified with the Erastus of Acts & 2 Tim, then - precisely because of his lifestyle as a pauline traveling companion - he could surely have managed any other city in which Paul might have met him, and simply held on to the nickname.
Thus, the traditional view, that Erastus the traveling companion was also (somehow?) a city-manager of Corinth - this should be firmly and completely rejected. At the very least, no man could have simultaneously remained BOTH one who traveled to Ephesus and Macedonia, doing apostolic/evangelistic business alongside Paul and Timothy AND one who displayed enough civic devotion within Corinth (or any other town, for that matter) for the local authorities and/or aristocracy to support his appointment as city-manager. Nor could any man have come back from such travels [adopting a foreign religion and leaving town for a long while simply for that devotion] to then gain the appointment as city manager. That simply would not have happened, and especially not in economically mighty Corinth.
In sum, the full identification of all three Erastus citations is a classic example wistful harmonization that's devoid of real historical thinking. It's also somewhat convenient for institutional preferences.
Putting the Acts & 2 Tim Erastus into Romans provides two things that appeal to established religious authorities. First, Erastus being the city manager of Corinth suggests the Corinthian church must have survived their struggles after both of Paul's letters, even up to the days of 2Tim. That's comforting (and possibly essential) if your job is to maintain status quo. Second, stringing Erastus from Romans to 2 Tim leaves a formerly traveling man now sitting in one spot for a very long time. Much like the anachronistic references to Timothy becoming "pastor" of Ephesus, this helps support a cessationist view of apostles and other itinerant workers.
Traveling ministers ought to stop and remain in one place for the rest of their lives. Also, Churches always stay together, being ruled by their local authorities. Yes, I do think that's a bit too much to put onto poor old Erastus, but it appears that this is what's been put onto him.
None of that, however, is the main problem I have with the mis-identification of Erastus.
The real reason I can't stand this awful slight is because it obscures what I happen to think is a clearer view of what most likely happened in Corinth. And this clearer view is more reasonable, more plausible, more supported by the text, less wistful, more accurately representative of how divine life in a people-group actually operates here on Earth most of the time, and - this view really ought to be - therefore more encouraging to the kind of corporate experiences and struggles we're all likely to face in something approaching genuinely organic* church life.
(See also: "The Death and Resurrection of Corinth, Parts 1, 2 & 3", which provides my own historical interpretation from the evidence, and will be posting this weekend.)
In conclusion, therefore, please take note. We have logical reasons for concluding that Erastus in Acts and Erastus in 2nd Timothy sound like the same kind of a man. We have no good reason for concluding that Erastus-the-city-manager was the same man as the travelling companion of Paul and Timothy. But if he was, then the name must belong to some post he'd held long years before. That is, if the traveling Erastus did just happen to be in Cenchrea with Paul when his Romans was written, then he most likely arrived there and kept moving along from there, just as Paul did.
In other words, the man named in Romans was probably merely a former city-manager, and there's no reason to think Corinth was necessarily the city he'd managed. But of the man named in 2 Tim, for it to have been noteworthy that he'd been "left behind", such a man must have been typically mobile. Thus, the Erastus of 2 Tim 4 implicitly seems like the same man as in Acts 19, but the Romans 16 reference adds nothing analogous to this same picture. They were probably two different men.
*Please forgive the trendiness of the term "organic". It's still the most precise one to use there, above.