Trying not to weigh in too heavily on this one as most arguments with respect to what ‘tongues’ is or isn’t can be found on other threads, but just a quick note -
“What do you think about the instances after Acts 2 in which believers spoke in tongues? These aren't identified as specific languages.”
No, they are not specifically identified. To me, there are two simple reasons for this: either the disciples/apostles who were there and later related the incident(s) did not recognize the language, or, given where the incident took place, the language in question was common knowledge; it didn’t need to be specifically stated. It was just one the disciples administering to these people did not speak. Between themselves, both parties involved would have used Greek as the common language (as both parties would have spoken it in various degrees of fluency).
If you’re thinking of something like Ephesus, keep in mind, like Corinth, it was a seaport and a major cultural crossroads. In addition, it was also home to one of the seven wonders of the ancient world; the temple of Artemis. In short, there would have been people there from all over the known world. It seems likely, given the reported narrative of Paul’s encounter, the folks he met were not native Ephesians; thus, not native speakers of Greek. They simply reacted to the situation in their native language – the narrative is silent as to what that language was. Why? Since it wasn't one known to Paul or his companions, they obviously could not report what it was; hence, why it is never named in the narrative. No modern tongues-speech here, just an unnamed rational language.
In any event, in all of these instances, what was spoken was real, rational language; not modern tongues-speech.