A bathtub curve is also memoryless though, and the back portion can be exponential. Consider two sub-populations of the same hardware. The first is small, evaded QA, and will fail early. Failures follow an exponential fall off. The second is much larger and failures rise exponentially with age.
Also consider mixing in "was dropped during shipping" or "was stored improperly".
My mistake, it seems I misunderstood what OP meant by that. Ignore that semantic detail and my position still stands. You've got a mix of subpopulations and many of the failure modes are definitely time dependent in some manner at least in the real world.
Also consider mixing in "was dropped during shipping" or "was stored improperly".