It is economically true in aggregate, although you're right that the worker overseeing the intern very often feels like it isn't true. The mechanic you mentioned could fall into that category, but I think it's more likely that it's just one of those jobs that's not knowledge work so what I'm saying doesn't really apply, because there are physical space limits to collaboration in realspace work that are much more readily obtrusive than equivalents in knowledge work. Basically, good knowledge worker A & bad knowledge worker B are never going to be "A + B" productive together, but they're also extremely unlikely to be <A productive, only in very specific situations that generally have to do with destructive operations by B (deleting files, using up limited tools like licenses or submissions, etc), and LLMs have been built specifically to not be able to engage in destructive operations. Contrast that with physical work, where two people can't physically occupy the same space and if they try they are likely to end up at a lower productivity than either one of them could have achieved alone because they quite literally trip over each other.
About the interns as hiring component, that's the official reason for interns and they are used that way, but they are also just valuable in and of themselves as labour. Companies that aren't even hiring and won't be in six months will still take on interns, because it's free labour. Interns are the equivalent of manual labourers in knowledge work, able to do what you tell them but not yet possessing the skills to do many complex tasks alone.
And I wouldn't be so sure that the "LLMs as interns" relationship we have now doesn't result in them learning. Obviously on an architecture level any individual instance can only learn in-context and that's wiped when the context is, but in aggregate they are learning from their "time on the job". The next version of GPT is going to be directly better at least partially because of all of the data that ChatGPT 4 being an effective intern brings in. It could be anywhere from just an intern at 6 months rather than an intern on the first week, through to an actual hired employee somewhere during their first year. Even if it was technologically possible I don't think OpenAI would deploy their next product if it was as good as a senior employee in some substantial number of domains, because that would be too disruptive of a leap for society. But anywhere on the intern scale that's better than GPT-4 up to approximately an employee one year in I think is feasible for their next release, and that will be in large part thanks to the data they get from their current deployment.