Rarely isn't never. That's not a substitute for an argument and I observe you don't even attempt to give an example where this would be an actual correct choice. I have a good guess why. This format is guaranteed by design to produce a stilted, low-information content essay that is neither informative, nor persuasive, nor entertaining, moreso than an essay freed from the artificially-imposed shackle of "we need an essay format that can be rapidly graded by people in an objective manner without reference to the actual content, indeed perhaps even by computer". Which is, after all, where the 5-paragraph form comes from, and why it lives. It really shouldn't be that surprising why it's such a bad idea to use it for anything you're not being graded on (and graded so superficially, too).

One might as well try to defend scales as being a valid form of music that should be performed in front of thousands of people. (And I mean literal, raw scales, not something that works a scale into a piece, for which there is no meaningful equivalent in this writing context.) Even if someone did that, it would be as some sort of artistic comment on listeners or the nature of art or something (see 4'33"), not because they have any reason to be performed in front of an audience.

By the way, since this may seem a bizarre amount of passion on the topic, what cheeses me off is that we TEACH this as the One True Essay Format. (See the beginning of the linked story.) I just can't believe the unnecessary harm we do with this. Even with my relatively low opinion of the ability of current formal schooling to educate, this still surprises me as a bizarre choice. So if I sound like I'd like everyone reading this to come away with the idea that this format ought to have a stake driven through it and you should never use it, it's just my feeble attempt to undo years of terrible schooling in a handful of paragraphs.