I believe you are wrong - it is increasingly ironic every time it is repeated. And doubly so given that 'to coin a phrase' is also a cliche. Whether that was their intention, or whether you are annoyed by it, is a different matter.
We're violently agreeing here. They're intending one irony and falling flat. That's an irony, but they get no credit from me. It wasn't their idea. And they're cunts.
I salute your (almost extinct) use of "coin the phrase/term" in a way that recognises the meaning.
People who add "to coin a phrase/term" after using a cliché, entirely unironically. Although they're not actually as bad as the ones who do it ironically - it was only ironic the first time somebody did it, you cunts. You're on Morissette levels of unironic when you try it.