Balaam's ass and a boozy bovine

Our regular correspondent Claude Tusk has just asked us the following question:

We learned today in Daf Yomi (Bava Kamma 35a) of Rav Papa's intelligent ox. Unlike the mouth of Balaam's ass in Avot 5:8, this ox did not require a special act of creation. What does that say about the place of speech in the hierarchy of cognition?

By way of background, the mouth of Balaam’s ass is listed in Avot 5:8 as one of 10 (or possibly as many as 13) objects created on Friday evening just before the onset of Shabbat. The reference to Rav Papa’s ox runs like this, according to a slightly edited version of the Soncino translation:

The case considered here is one of an intelligent animal which, owing to an itching in the back, was anxious to burn a barn so that it might roll in the [hot] ashes [and thereby gain relief]. But how could we know [that the animal possessed such an intention]? [By seeing that] after the barn had been burnt, the animal actually rolled in the ashes. But could such a thing ever happen? — Yes, as in the case of the ox which had been in the house of R. Papa and which, having a severe toothache, went into the brewery, where it removed the lid [that covered the beer] and drank beer until it became relieved [of the pain].

So why, then, does the mishnah include the mouth of the ass but exclude the potential of members of the animal kingdom to develop their intellect?

Before I give my own answer, which I propose to do on Sunday, I’d like to hear from readers. What do you think?