While I’ve seen lots of snappy, short, intelligent, and witty pieces of academic writing, I feel like people who criticize academic writing are really complaining about several different tendencies that rarely occur in the same piece of writing, all of which occur more often in academic writing than in most other kinds.
One tendency is to use specialized jargon. This makes perfect sense — terminology is invented in order to quickly reference a nuanced idea, at the cost of being impenetrable to people unfamiliar with the nuanced idea (and thus unfamiliar with the term). Using jargon as a shibboleth is also not without merit — explaining the meaning of these terms requires explaining the ideas behind them, which takes time and energy & is a waste of effort when the readership is already familiar with them; excluding readers without the prerequisite background to understand nuanced points is perfectly reasonable, particularly when good resources exist to bring a general audience up to speed on the ideas and terms. People working in the depths are not necessarily the best popularizers, and they don’t need to be.
Another tendency is to draw arguments out, making explanations overly long. I feel like this comes out of either avoiding jargon or not having access to the appropriate jargon.
A third tendency bears superficial resemblance to the first two, and is genuine obscurantism. This is a lot less common in academic writing than a lot of people think; it’s pretty common in business.
A fourth tendency, related to tendency number one, is to mimic the formal structures common in one’s field even when they are inappropriate for the task at hand. I don’t think that extreme examples of this are very common — academics are human beings, too, and can tell when something really isn’t working. But, how egregious examples of this appear depends heavily upon how familiar with the common structures the reader is — even something almost universal, like the format of a scientific paper with its list of references at the end and its abstract, can seem strange and awkward to someone who has never read one before. Again, the skill-set for communicating with a general audience is different from the skill-set for communicating with academics in the same field, and while some people have both skill-sets, they do not necessarily write a single document for both audiences.
(It’s also useful to note that some of the most entertaining academic work plays with the jargon and the structure in use in the field in a playful and perverse way. Single-line published papers and theorems, for instance, do this and are sometimes extremely influential. But, these things are even less accessible to a general audience.)