I would have put it a little differently. It seems more about image to me than strictly "joking isn't appropriate in business." Apple has an image that is one of sleek, refined beauty. The style of writing used in
this article would totally clash with that, causing nothing but confusion and weak branding.
On the other hand, there are brands out there with the exact opposite approach. Cards Against Humanity comes to mind first. Their image is explicitly one of mild carelessness and apparent candidness such that anything written too formally would seem out of place.
But indeed, there do seem to be more of the former brand type than of the latter. Having a neighbor who speaks constantly with a similar tone as the writer of this article, I can say that trying to hold my own in a conversation with him is really tiring. You eventually just run out of witty remarks. Is it possible it's more an issue of skill and time? As in, are there fewer people out there with the skills necessary to make good silly writing than there are people who can write seriously? And does it take them longer (and thus cost even more) to make writing in this style?
I rambled a little, but I think the issue is a combination of people equating seriousness with importance, as well as a general lack of creativity.