The hyperbole reading is special pleading invented under moral pressure
The objection
Notice when this reading became popular. It is not a discovery of the last century's archaeology being applied to a neutral question; it arrives precisely as the moral objection becomes unbearable to defend head-on, and it arrives from people who need the text not to say what it says. That is the classic profile of a rationalization. And it is applied selectively: the same reader takes the promises literally, the miracles literally, the resurrection literally, and then discovers that the one category of text he finds embarrassing is idiomatic. A rule invoked only where it rescues you is not a rule of interpretation.
The response
The suspicion is fair and the timing point has some force, so the reply has to be evidence that does not depend on anyone's motives. Three pieces. First, the comparative material was not produced to solve this problem: Merneptah's stele and the Mesha stone were dug up and read for their own sake, and both make total-annihilation claims that are simply false about peoples who kept existing. That is the convention, documented in someone else's writing, about someone else's wars. Second, the internal evidence is not a modern reading at all — the Anakim are destroyed and then found in three cities one verse later, and Judges opens by listing who was not driven out. Those sentences have been sitting next to each other for as long as the books have existed. Third, the selectivity charge can be tested rather than asserted: the standard being applied is that a text's genre governs how it is read, which is why nobody reads the Psalms' mountains skipping like rams as zoology. Whether that standard is being applied honestly here is a fair thing to check, and the check is the internal evidence, which is public. Where the objection lands and stays landed: even if the rhetoric reading is entirely correct about the numbers, it does not touch the command, which is the next objection and the more serious one.