We come back to the original argument, which is that at-least-once delivery of idempotent operations is how you represent things that should happen exactly once in a system, and in a saner world this could reasonably be called exactly-once delivery.
Every distributed systems engineer knows what "exactly-once delivery" is asking for, and in plain English it's valid to conflate the two, but for some reason the field has decided to treat the phrase as an annoying semantic pit trap for the unwary. Want to add an ID to your transactions to make them idempotent? Well, even though your transactions are now recorded exactly once, that wasn't technically delivery! Gotcha!
The issue is precision in terminology and resulting understanding. At-least-once delivery with idempotency imposes certain rules on the processing of messages. As you say, every distributed systems engineer knows this.
When you call something exactly-once, people who are perhaps not distributed systems engineers make the reasonable assumption that this means exactly what it says. They will engineer around this reasonable assumption based on a clear technical description and get something hilariously broken in non-obvious ways. This will have happened because jargon ("exactly-once delivery") has been confused for a technical description of a delivery system's properties.
Not everyone in this series of comments is a distributed systems engineer. Never mind everyone using a messaging system.
If you zoom out enough then every system looks like a black box and the only thing that matters is inputs and outputs. Messaging systems are no different in that respect from literally everything else. If you're building a messaging system, there's a world of difference in terms of how other people integrate with your software if you say "exactly-once" vs "at-least-once."
Every distributed systems engineer knows what "exactly-once delivery" is asking for, and in plain English it's valid to conflate the two, but for some reason the field has decided to treat the phrase as an annoying semantic pit trap for the unwary. Want to add an ID to your transactions to make them idempotent? Well, even though your transactions are now recorded exactly once, that wasn't technically delivery! Gotcha!