I don't know. There are probably times where you'd want to do less damage to a monster.
There are probably a few monsters where the quiver is a slight advantage over any of the half/half elemental quivers or just doing physical with the Quiver of Infinity. Checking the hunter's guide, I'd say the Exodus Minion is probably one for this list. It averages two high resists (physical, fire) and three low resists (energy, cold, poison). With a half/half elemental, you are hitting 50% against a high and 50% against a low at best. With a Quiver of Rate, you are hitting 40% against a high and 60% against a low.
I would argue that the Minion is the exception rather than the rule. Something with 100% poison resist for example (The Dread Spider) basically takes 20% less damage. Since very few monsters have 100% physical (none to my knowledge), the Quiver of Infinity is usually a better bet with its other properties unless you know the resists of what you are fighting specifically.